Jein-Shan Chen

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Jein-Shan verified their affiliation via an institutional email.

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• Ph.D., Univ. of Washington
• Professor at National Taiwan Normal University

Two novel ways to generate closed convex cones, the main ingredient of conic optimization, are proposed in this study. The first way is constructing closed convex cones via inequalities, whereas the second one is through support functions. The contribution of this article is twofold. One is opening up new ideas for looking into structures of closed...

In this paper, we propose a specific dynamical model for solving a class of vector equilibrium problems with partial order induced by a polyhedral cone which is generated by some matrix. Unlike the traditional dynamical models, it particularly possesses the feature of fractional-order system. The so-called Mittag-Leffler stability of the dynamical...

In this paper, we investigate a class of quasi-hemivariational inequalities involving the generalized subdifferentials in the sense of Clarke and the set-valued constraint in the setting of constant curvature Hadamard manifolds. Using the Kakutani-Fan-Glicksberg type fixed point theorem for multi-valued maps on Hadamard manifolds, we prove the none...

The aim of this paper is to investigate the difference gap (for brevity, D-gap) functions and global error bounds for an abstract class of elliptic variational-hemivariational inequalities (for brevity, EVHIs). Based on the optimality condition for the concerning minimization problem, the regularized gap function for EVHIs is proposed under some su...

In this paper, we propose a smoothing penalty approach for solving the second-order cone complementarity problem (SOCCP). The SOCCP is approximated by a smooth nonlinear equation with penalization parameter. We show that any solution sequence of the approximating equations converges to the solution of the SOCCP under the assumption that the associa...

Strongly motivated from applications in various fields including machine learning, the methodology of sparse optimization has been developed intensively so far. Especially, the advancement of algorithms for solving problems with nonsmooth regularizers has been remarkable. However, those algorithms suppose that weight parameters of regularizers, cal...

The main purpose of this paper is to investigate the upper bound and Hölder continuity for a general class of parametric elliptical variational-hemivariational inequalities via regularized gap functions. More precisely, we deliver a formulation of the elliptical variational-hemivariational inequalities in the case of the perturbed parameters govern...

In this paper, we study a new class of vector equilibrium problems associated with partial order provided by p-order cone on Hadamard manifolds. We first propose a new concept of K k p-convexity of a vector-valued function in the setting of Hadamard manifolds and derive some regularized gap functions of the concerning problem. Then, several upper b...

The aim of this paper is to study the difference gap function (for brevity, DG-function) and upper error bounds for an abstract class of variational-hemivariational inequalities with history-dependent operators (for brevity, HDVHIs). First, we propose a new concept of gap functions to the HDVHIs and consider the regularized gap function (for brevit...

In this paper, we will study about the solvability and duality of interval optimization problems on Hadamard manifolds. It includes the KKT conditions, and Wofle dual problem with weak duality and strong duality. These results are the complement for the solvability of interval optimization problems on Hadamard manifolds.

A novel approach for solving the general absolute value equation \(Ax+B|x| = c\) where \(A,B\in \textrm{I}\! \textrm{R}^{m\times n}\) and \(c\in \textrm{I}\! \textrm{R}^m\) is presented. We reformulate the equation as a nonconvex feasibility problem which we solve via the method of alternating projections (MAP). The fixed points set of the alternat...

We present a new approach which combines smoothing technique and semi-proximal alternating direction method of multipliers for image deblurring. More specifically, in light of a nondifferentiable model, which is indeed of the hybrid model of total variation and Tikhonov regularization models, we consider a smoothing approximation to conquer the dis...

The goal of this paper is to investigate the curves intersected by a vertical plane with the surfaces based on certain NCP functions. The convexity and differentiability of these curves are studied as well. In most cases, the inflection points of the curves cannot be expressed exactly. Therefore, we instead estimate the interval where the curves ar...

Based on a class of smoothing approximations to projection function onto second-order cone, an approximate lower order penalty approach for solving second-order cone linear complementarity problems (SOCLCPs) is proposed, and four kinds of specific smoothing approximations are considered. In light of this approach, the SOCLCP is approximated by asym...

In this article, we introduce the interval optimization problems (IOPs) on Hadamard manifolds as well as study the relationship between them and the interval variational inequalities. To achieve the theoretical results, we build up some new concepts about $gH$-directional derivative and $gH$-G\^ateaux differentiability of interval valued functions...

Weighted low-rank Hankel matrix optimization has long been used to reconstruct contaminated signal or forecast missing values for time series of a wide class. The Method of Alternating Projections (MAP) (i.e., alternatively projecting to a low-rank matrix manifold and the Hankel matrix subspace) is a leading method. Despite its wide use, MAP has lo...

We present a new class of neural networks for solving nonlinear complementarity problems (NCPs) based on some family of real-valued functions (denoted by ℱ) that can be used to construct smooth perturbations of the level curve defined by ΦNR(x,y)=0, where ΦNR is the natural residual function (also called the “min” function). We introduce two import...

In this paper, we suggest the Levenberg-Marquardt method with Armijo line search for solving absolute value equations associated with the second-order cone (SOCAVE for short), which is a generalization of the standard absolute value equation frequently discussed in the literature during the past decade. We analyze the convergence of the proposed al...

In contrast to symmetric cone optimization, there has no unified framework for non-symmetric cone optimization. One main reason is that the structure of various non-symmetric cone differs case by case. Especially, their boundary conditions are usually mysterious. In this paper, we provide characterizations of boundary conditions on some non-symmetr...

Strongly motivated from use in various fields including machine learning, the methodology of sparse optimization has been developed intensively so far. Especially, the recent advance of algorithms for solving problems with nonsmooth regularizers is remarkable. However, those algorithms suppose that weight parameters of regularizers, called hyperpar...

A novel approach for solving the general absolute value equation $Ax+B|x| = c$ where $A,B\in \mathbb{R}^{m\times n}$ and $c\in \mathbb{R}^m$ is presented. We reformulate the equation as a feasibility problem which we solve via the method of alternating projections (MAP). The fixed points set of the alternating projections map is characterized under...

In this paper, we propose a new smoothing strategy along with conjugate gradient algorithm for the signal reconstruction problem. Theoretically, the proposed conjugate gradient algorithm along with the smoothing functions for the absolute value function is shown to possess some nice properties which guarantee global convergence. Numerical experimen...

The P-property of the linear transformation in second-order cone linear complementarity problems (SOCLCP) plays an important role in checking the globally uniquely solvable (GUS) property due to the work of Gowda et al. However, it is not easy to verify the P-property of the linear transformation, in general. In this paper, we provide matrix charac...

We propose an efficient neural network for solving the second-order cone constrained variational inequality (SOCCVI). The network is constructed using the Karush-Kuhn-Tucker (KKT) conditions of the variational inequality (VI), which is used to recast the SOCCVI as a system of equations by using a smoothing function for the metric projection mapping...

The natural residual (NR) function is a mapping often used to solve nonlinear complementarity problems (NCPs). Recently, three discrete-type families of complementarity functions with parameter p⩾3 (where p is odd) based on the NR function were proposed. Using a neural network approach based on these families, it was observed from some preliminary...

We report a new method to construct complementarity functions for the nonlinear complementarity problem (NCP). Basic properties related to growth behavior, convexity and semismoothness of the newly discovered NCP functions are proved. We also present some variants, generalizations and other transformations of these NCP functions. Finally, we propos...

It is known that the analysis to tackle with non-symmetric cone optimization is quite different from the way to deal with symmetric cone optimization due to the discrepancy between these types of cones. However, there are still common concepts for both optimization problems, for example, the decomposition with respect to the given cone, smooth and...

The l1-norm regularized minimization problem is a non-differentiable problem and has a wide range of applications in the field of compressive sensing. Many approaches have been proposed in the literature. Among them, smoothing l1-norm is one of the effective approaches. This paper follows this path, in which we adopt six smoothing functions to appr...

The second-order tangent set is an important concept in describing the curvature of the set involved. Due to the existence of the complementarity condition, the second-order cone (SOC) complementarity set is a nonconvex set. Moreover, unlike the vector complementarity set, the SOC complementarity set is not even the union of finitely many polyhedra...

In this paper, we consider a family of neural networks for solving nonlinear complementarity problems (NCP). The neural networks are constructed from the merit functions based on three classes of NCP-functions: the generalized natural residual function and its two symmetrizations. In this paper, we first characterize the stationary points of the in...

In this article, we study the second-order optimality conditions for a class of circular conic optimization problem. First, the explicit expressions of the tangent cone and the second-order tangent set for a given circular cone are derived. Then, we establish the closed-form formulation of critical cone and calculate the “sigma” term of the aforeme...

In this paper, we summarize several systematic ways of constructing smoothing functions and illustrate eight smoothing functions accordingly. Then, based on these systematically generated smoothing functions, a unified neural network model is proposed for solving absolute value equation. The issues regarding the equilibrium point, the trajectory, a...

This paper focuses on solving the quadratic programming problems with second-order cone constraints (SOCQP) and the second-order cone constrained variational inequality (SOCCVI) by using the neural network. More specifically, a neural network model based on two discrete-type families of SOC complementarity functions associated with second-order con...

In this chapter, we will see details about how the characterizations established in Chap. 2 be applied in real algorithms. In particular, the SOC-convexity are often involved in the solution methods of convex SOCPs; for example, the proximal-like methods. We present three types of proximal-like algorithms, and refer the readers to [115, 116, 118] f...

During the past two decades, there have been active research for second-order cone programs (SOCPs) and second-order cone complementarity problems (SOCCPs). Various methods had been proposed which include the interior-point methods [1, 102, 109, 123, 146], the smoothing Newton methods [51, 63, 71], the semismooth Newton methods [86, 120], and the m...

In this chapter, we introduce the SOC-convexity and SOC-monotonicity which are natural extensions of traditional convexity and monotonicity. These kinds of SOC-convex and SOC-monotone functions are also parallel to matrix-convex and matrix-monotone functions, see [21, 74]. We start with studying the SOC-convexity and SOC-monotonicity for some simpl...

In this chapter, we present some other types of applications of the aforementioned SOC-functions, SOC-convexity, and SOC-monotonicity. These include so-called SOC means, SOC weighted means, and a few SOC trace versions of Young, Hölder, Minkowski inequalities, and Powers–Størmer’s inequality. We believe that these results will be helpful in converg...

It is known that the concept of convexity plays a central role in many applications including mathematical economics, engineering, management science, and optimization theory. Moreover, much attention has been paid to its generalization, to the associated generalization of the results previously developed for the classical convexity, and to the dis...

In this paper, we look into the detailed properties of four discrete- type families of NCP-functions, which are newly discovered in recent literature. With the discrete-oriented feature, we are motivated to know what differences there are compared to the traditional NCP-functions. The properties obtained in this paper not only explain the differenc...

In this paper, we derive a few type of trace versions of Young in- equality associated with second-order cone, which can be applied to derive the Holder inequality, Minkowski inequality. Moreover, the triangular inequality is also considered.

This book covers all of the concepts required to tackle second-order cone programs (SOCPs), in order to provide the reader a complete picture of SOC functions and their applications. SOCPs have attracted considerable attention, due to their wide range of applications in engineering, data science, and finance. To deal with this special group of opti...

In this paper, we illustrate a new concept regarding unitary elements defined on Lorentz cone, and establish some basic properties under the so-called unitary transformation associated with Lorentz cone. As an application of unitary transformation, we achieve a weaker version of the triangle inequality and several (weak) majorizations defined on Lo...

In this paper, we define various means associated with Lorentz cones (also known as second-order cones), which are new concepts and natural extensions of traditional arithmetic mean, harmonic mean, and geometric mean, logarithmic mean. Based on these means defined on the Lorentz cone, some inequalities and trace inequalities are established.

In this paper, we explore a unified way to construct smoothing functions for solving the absolute value equation associated with second-order cone (SOCAVE). Numerical comparisons are presented, which illustrate what kinds of smoothing functions work well along with the smoothing Newton algorithm. In particular, the numerical experiments show that t...

It is well known that complementarity functions play an important role in dealing with complementarity problems. In this paper, we propose a few new classes of complementarity functions for nonlinear complementarity problems and second-order cone complementarity problems. The constructions of such new complementarity functions are based on discrete...

The class of ellipsoidal cones, as an important prototype in closed convex cones, covers several practical instances such as second-order cone, circular cone and elliptic cone. In natural feature, it belongs to the category of nonsymmetric cones because it is non-self-dual under standard inner product. Nonetheless, it can be converted to a second-o...

This paper surveys two neural networks for solving nonlinear convex programs with the second-order cone constraints. The neural network models are designed based on two different C-functions associated with a second-order cone. Various stabilities along with the neural networks are presented. Numerical comparisons are also reported.

In this paper, we propose two new smooth support vector machines for \(\varepsilon \)-insensitive regression. According to these two smooth support vector machines, we construct two systems of smooth equations based on two novel families of smoothing functions, from which we seek the solution to \(\varepsilon \)-support vector regression (\(\vareps...

The circular cone ℒ𝜃\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {L}_{\theta }$\end{document} is not self-dual under the standard inner product and includes...

Merit function approach is a popular method to deal with complementarity problems, in which the complementarity problem is recast as an unconstrained minimization via merit function or complementarity function. In this paper, for the complementarity problem associated with p-order cone, which is a type of nonsymmetric cone complementarity problem,...

In this paper, we consider the smoothing Newton method for solving a type of absolute value equations associated with second order cone (SOCAVE for short), which is a generalization of the standard absolute value equation frequently discussed in the literature during the past decade. Based on a class of smoothing functions, we reformulate the SOCAV...

In this short paper, we look into a conclusion drawn by Alzalg (J Optim Theory Appl 169:32–49, 2016). We think the conclusion drawn in the paper is incorrect by pointing out three things. First, we provide a counterexample that the proposed inner product does not satisfy bilinearity. Secondly, we offer an argument why a pth-order cone cannot be sel...

In this paper, we study the parabolic second-order directional derivative in the Hadamard sense of a vector-valued function associated with circular cone. The vector-valued function comes from applying a given real-valued function to the spectral decomposition associated with circular cone. In particular, we present the exact formula of second-orde...

It is well known that the second-order cone and the circular cone have many analogous properties. In particular, there exists an important distance inequality associated with the second-order cone and the circular cone. The inequality indicates that the distances of arbitrary points to the second-order cone and the circular cone are equivalent, whi...

The system of absolute value equation, denoted by AVE, is a non-differentiable NP-hard problem. Many approaches have been proposed during the past decade and most of them focus on reformulating it as complementarity problem and then solve it accordingly. Another approach is to recast the AVE as a system of nonsmooth equations and then tackle with t...

It is well known that second-order cone (SOC) programming can be regarded as a special case of positive semidefinite programming using the arrow matrix. This paper further studies the relationship between SOCs and positive semidefinite matrix cones. In particular, we explore the relationship to expressions regarding distance, projection, tangent co...

This paper proposes a neural network approach to efficiently solve nonlinear convex programs with the second-order cone constraints. The neural network model is designed by the generalized Fischer-Burmeister function associated with second-order cone. We study the existence and convergence of the trajectory for the considered neural network. Moreov...

In this paper, we consider a particular conic optimization problem over nonsymmetric circular cone. This class of optimization problem has been found useful in optimal grasping manipulation problems for multi-fingered robots. We first introduce a pair of logarithmically homogeneous self-concordant barrier function for circular cone and its dual con...

Symmetric cone (SC) monotone functions and SC-convex functions are real scalar valued functions which induce Löwner operators associated with a simple Euclidean Jordan algebra to preserve the monotone order and convex order, respectively. In this paper, for a general simple Euclidean Jordan algebra except for octonion case, we show that the SC-mono...

It is known that complementarity functions play an important role in dealing with complementarity problems. The most well known complementarity problem is the symmetric cone complementarity problem (SCCP) which includes nonlinear complementarity problem (NCP), semidefinite complementarity problem (SDCP), and second-order cone complementarity proble...

In this paper, we consider complementarity problem associated with circular cone, which is a type of nonsymmetric cone complementarity problem. The main purpose of this paper is to show the readers how to construct complementarity functions for such nonsymmetric cone complementarity problem, and propose a few merit functions for solving such a comp...

Let \(\mathcal{L}_{\theta }\) be the circular cone in \({\mathbb {R}}^n\) which includes second-order cone as a special case. For any function f from \({\mathbb {R}}\) to \({\mathbb {R}}\) , one can define a corresponding vector-valued function \(f^{\mathcal{L}_{\theta }}\) on \({\mathbb {R}}^n\) by applying f to the spectral values of the spectral...

In this paper, we consider a type of cone-constrained convex program in finite-dimensional space, and are interested in characterization of the solution set of this convex program with the help of the Lagrange multiplier. We establish necessary conditions for a feasible point being an optimal solution. Moreover, some necessary conditions and suffic...

In contrast to the generalized Fischer-Burmeister function that is a natural extension of the popular Fischer-Burmeister function NCP-function, the generalized natural residual NCP-function based on discrete extension, recently proposed by Chen, Ko, and Wu, does not possess symmetric graph. In this paper we symmetrize the generalized natural residu...

In this paper, we study the existence of local and global saddle points for nonlinear second-order cone programming problems. The existence of local saddle points is developed by using the second-order sufficient conditions, in which a sigma-term is added to reflect the curvature of second-order cone. Furthermore, by dealing with the perturbation o...

The circular cone is a pointed closed convex cone having hyperspherical sections orthogonal to its axis of revolution about which the cone is invariant to rotation, which includes second-order cone as a special case when the rotation angle is 45 degrees. Let Lθ denote the circular cone in Rn. For a function f from R to R, one can define a correspon...

This paper proposes a neural network approach for efficiently solving general nonlinear convex programs with second-order cone constraints. The proposed neural network model was developed based on a smoothed natural residual merit function involving an unconstrained minimization reformulation of the complementarity problem. We study the existence a...

In this paper, we study geometric properties of surfaces of the generalized Fischer–Burmeister function and its induced merit function. Then, a visualization is proposed to explain how the convergent behaviors are influenced by two descent directions in merit function approach. Based on the geometric properties and visualization, we have more intui...

The editors of this special issue would like to express their gratitude to the authors who have submitted manuscripts for consideration. They also thank the many individuals who served as referees of the submitted manuscripts.

It has been an open question whether the family of merit functions ψ p (p>1), the generalized Fischer-Burmeister (FB) merit function, associated to the second-order cone is smooth or not. In this paper we answer it partly, and show that ψ p is smooth for p∈(1,4), and we provide the condition for its coerciveness. Numerical results are reported to i...

In this paper, we investigate the issue of error bounds for symmetric cone complementarity problems (SCCPs). In particular, we show that the distance between an arbitrary point in Euclidean Jordan algebra and the solution set of the symmetric cone complementarity problem can be bounded above by some merit functions such as Fischer-Burmeister merit...

The study of this paper consists of two aspects. One is characterizing the so-called circular cone convexity of f by exploiting the second-order differentiability of fLθ; the other is introducing the concepts of determinant and trace associated with circular cone and establishing their basic inequalities. These results show the essential role playe...

Circular cone includes second-order cone as a special case when the rotation angle is 45 degree. This paper gives an insight on circular cone, in which we describe the tangent cone, normal cone, second order tangent cone, and second order regularity of circular cone. Moreover, we establish the spectral factorization associated with circular cone. T...

Let LθLθ be the circular cone in RnRn which includes a second-order cone as a special case. For any function ff from RR to RR, one can define a corresponding vector-valued function fc(x) on RnRn by applying ff to the spectral values of the spectral decomposition of x∈Rnx∈Rn with respect to LθLθ. We show that this vector-valued function inherits fro...

Let K be the symmetric cone in a Jordan algebra ¥. For any function f from ]R to 1R,one can define the corresponding Löwner function fsc(x) on ¥ by the spectral decomposition of x ε ¥ with respect to 1C. In this paper, we study the relationship regarding. H-differentiability between fsc and f. The class of if-differentiable functions is known to be...

This paper investigates the set-valued complementarity problems (SVCP) which poses rather different features from those that classical complementarity problems hold, due to tthe fact that he index set is not fixed, but dependent on x. While comparing the set-valued complementarity problems with the classical complementarity problems, we analyze the...

We would like to express our gratitude to all the authors for their contribution and collaboration and to the many reviewers for their valuable comments, suggestions, and timely responses.

This paper is a counterpart of Bi et al., 2011. For a locally optimal solution to the nonlinear second-order cone programming (SOCP), specifically, under Robinson’s constraint qualification, we establish the equivalence among the following three conditions: the nonsingularity of Clarke’s Jacobian of Fischer-Burmeister (FB) nonsmooth system for the...

Multifingered robots play an important role in manipulation applications. They can grasp various shaped objects to perform point-to-point movement. It is important to plan the motion path of the object and appropriately control the grasping forces for multifingered robot manipulation. In this paper, we perform the optimal grasping control to find b...

This paper is devoted to the study of the proximal point algorithm for solving monotone and nonmonotone nonlinear complementarity problems. The proximal point algorithm is to generate a sequence by solving subproblems that are regularizations of the original problem. After given an appropriate criterion for approximate solutions of subproblems by a...

In this paper, we deal with the semi-infinite complementarity problems (SICP), in which several important issues are covered, such as solvability, semismoothness of residual functions, and error bounds. In particular, we characterize the solution set by investigating the relationship between SICP and the classical complementarity problem. Office. T...

In this paper, we establish convexity of some functions associated with symmetric cones, called SC trace functions. As illustrated in the paper, these functions play a key role in the development of penalty and barrier functions methods for symmtric cone programs.

In the paper, we consider a continuation approach for the binary quadratic program (BQP) based on a class of NCP-functions. More specifically, we recast the BQP as an equivalent minimization and then seeks its global minimizer via a global continuation method. Such approach had been considered in [11] which is based on the Fischer–Burmeister functi...

We establish that the Fischer–Burmeister (FB) complementarity function and the natural residual (NR) complementarity function associated with the symmetric cone have the same growth, in terms of the classification of Euclidean Jordan algebras. This, on the one hand, provides an affirmative answer to the second open question proposed by Tseng (J Opt...

This paper investigates the Lipschitz continuity of the solution mapping of symmetric cone (linear or nonlinear) complementarity problems (SCLCP or SCCP, resp.) over Euclidean Jordan algebras. We show that if the transformation has uniform Cartesian P-property, then the solution mapping of the SCCP is Lipschitz continuous. Moreover, we establish th...

The SOC-monotone function (respectively, SOC-convex function) is a scalar valued function that induces a map to preserve the monotone order (respectively, the convex order), when imposed on the spectral factorization of vectors associated with second-order cones (SOCs) in general Hilbert spaces. In this paper, we provide the sufficient and necessar...

In this paper, we provide an important application of the Schur Complement Theorem in establishing convexity of some functions associated with second-order cones (SOCs), called SOC-trace functions. As illustrated in the paper, these functions play a key role in the development of penalty and barrier functions methods for second-order cone programs,...

This paper is devoted to the study of the proximal point algorithm for solving monotone second-order cone complementarity problems. The proximal point algorithm is to generate a sequence by solving subproblems that are regularizations of the original problem. After given an appropriate criterion for approximate solutions of subproblems by adopting...

In this paper, we consider using the neural networks to efficiently solve the second-order cone constrained variational inequality (SOCCVI) problem. More specifically, two kinds of neural networks are proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of the SOCCVI problem. The first neural network uses the Fischer-Burmeister (FB) functi...

This paper makes a survey on SOC complementarity functions and related solution methods for the second-order cone programming (SOCP) and second-order cone complementarity problem (SOCCP). Specifically, we discuss the properties of four classes of popular merit functions, and study the theoretical results of associated merit function methods and num...

Let Kn be the Lorentz/second-order cone in IRn. For any function f from IR to IR, one can define a corresponding vector-valued function fsoc (x) on IRn by applying f to the spectral values of the spectral decomposition of x ∈ IRn with respect to Kn. It was shown by J.-S. Chen, X. Chen and P. Tseng in [5] that this vector-valued function inherits fr...

Submitted by J.A. Filar Keywords: Hilbert space Complementarity Second-order cone Merit functions We introduce the Jordan product associated with the second-order cone K into the real Hilbert space H, and then define a one-parametric class of complementarity functions Φ t on H × H with the parameter t ∈ [0, 2). We show that the squared norm of Φ t...

Given a Hilbert space HH, the infinite-dimensional Lorentz/second-order cone KK is introduced. For any x∈Hx∈H, a spectral decomposition is introduced, and for any function f:R→Rf:R→R, we define a corresponding vector-valued function fH(x)fH(x) on Hilbert space HH by applying ff to the spectral values of the spectral decomposition of x∈Hx∈H with res...

For a locally optimal solution to the nonlinear semidefinite programming problem, under Robinson's constraint qualification, we show that the nonsingularity of Clarke's Jacobian of the Fischer-Burmeister (FB) nonsmooth system is equivalent to the strong regularity of the Karush-Kuhn-Tucker point. Consequently, from Sun's paper [Math. Oper. Res., 31...

This paper proposes using the neural networks to efficiently solve the second-order cone programs (SOCP). To establish the neural networks, the SOCP is first reformulated as a second-order cone complementarity problem (SOCCP) with the Karush–Kuhn–Tucker conditions of the SOCP. The SOCCP functions, which transform the SOCCP into a set of nonlinear e...