Ubaldo Garcia

University of Vigo | UVIGO · Ingenieria de Telecomunicaciones

This paper presents a class of nonmonotone Direct Search Methods that converge to stationary points of unconstrained and boxed constrained mixed-integer optimization problems. A new concept is introduced: the quasi-descent direction. A point x is stationary on a set of search directions if there exists no feasible qdd on that set. The method does n...

This paper describes a non-monotone direct search method (NMDSM) that finds a stationary point of linearly constrained minimization problems. At each iteration the algorithm uses NMDSM techniques on the Euclidean space \({\mathbb {R}}^n\) spanned by n variables carefully selected from the \(n+m\) variables formulated by the model under analysis. Th...

This paper presents a unified convergence theory for non monotonous Direct Search Methods (DSMs), which embraces several algorithms that have been proposed for the solution of unconstrained and boxed constraints models. This paper shows that these models can be theoretically solved with the same methodology and under the same weak assumptions. All...

This paper is an outgrowth of previous works devoted to the application of non monotone direct search methods (DSMs) to locate the global minimum of an objective function subjected to bounds on its variables defined in the Euclidean space. This paper proves that DSMs can be easily adapted for solving models with discrete variables, as long as these...

Updated ”C” code for solving box-constrained models with discrete variables. Version 31

This article approaches the dynamic resource allocation problem for the downlink of a wireless mobile communication system (WMCS). The article defines the architecture and functions of the global resource scheduler, as well as the quality index for scheduling, the signal to interference-plus-noise ratio (SINR). The proposed approach divides the sch...

This article addresses the dynamic resource allocation problem (power and frequency resources) for the downlink of a multicell, multiservice mobile communication system with heterogeneous architecture, deployed into a urban environment, using OFDM (Orthogonal Frequency Division Multiplexing) at the physical level. The proposed optimization model ai...

This article treats the resource allocation problem for the downlink of a multi-cell, multiservice Wireless Mobile Communications System (WMCS) with heterogeneous architecture deployed into an urban environment using Long Term Evolution (LTE) and Orthogonal Frequency Division Multiple Access (OFDMA) in its physical level. The optimization model aim...

Recent work has focused on techniques to construct a learning machine able to classify, at any given accuracy, all members of two mutually exclusive classes. Good numerical results have been reported; however, there remain some concerns regarding prediction ability when dealing with large data bases. This paper introduces clustering, which decrease...

This paper presents an approach for solving the resource allocation problem in heterogeneous networks (HETnets). An optimization model is formulated; its main objective is to achieve the best Quality of Service (QoS) measured by the Carrier to Interference Noise Ratio (CINR). This model is a quadratically constrained optimization problem with conti...

In this paper we extend Continuous Derivative Free (CDF) algorithms that solve optimization models with continuous variables to the solution of optimization models with both continuous and discrete variables. The algorithm fits naturally to the solution of discretized models arising from continuous models. Roughly speaking, the finer the discretiza...

This paper proposes a space decomposition scheme for non-monotone (NM) derivative-free parallel and sequential algorithms for solving the box-constrained optimization problem (BCOP). Convergence to Karush Kuhn Tucker points is proved under the same conditions for NM and monotone algorithms for solving unconstrained and BCOPs. The parallel algorithm...

This work presents an algorithm that converges to points that satisfy a first-order necessary condition of weakly Pareto solutions of multiobjective optimization problems. Hints on how to include second-order information are given. Preliminary numerical results are encouraging.

In this paper, we study the application of non-monotone derivative-free optimization algorithms to wireless local area networks (WLAN) planning, which can be modeled as an unconstrained minimization problem. We wish to determine the access point (AP) positions that maximize coverage in order to provide connectivity to static and mobile users. As th...

Keywords Projections Relaxation Fejér Property Convergence of PPA Discussion See also References

Non monotone algorithms allow a possible increase of function values at certain iterations. This paper gives a suitable control on this increase to preserve the convergence properties of its monotone counterpart. A new efficient MultiLineal Search is also proposed for minimization algorithms.

This paper presents a general approach that combines global search strategies with local search and attempts to find a global minimum of a real valued function of n variables. It assumes that derivative information is unreliable; consequently, it deals with derivative free algorithms, but derivative information can be easily incorporated. This pape...

Non monotone algorithms allow a possible increase of function values at certain iterations. This paper gives a suitable control on this increase to preserve the convergence properties of its monotone counterpart. A new efficient MultiLineal Search is also proposed for minimization algorithms. Full Text at Springer, may require registration or fee

Large-scale Support Vector Machine (SVM) classification is a very active research line in data mining. In recent years, several efficient SVM generation algorithms based on quadratic problems have been proposed, including: Successive OverRelaxation (SOR), Active Support Vector Machines (ASVM) and Lagrangian Support Vector Machines (LSVM). These alg...

We propose a methodology to deploy large scale IEEE 802.11b telecommunications infrastructures, which are being currently used to provide broadband access in Spanish rural areas, as an expansion of shared asymmetric DVB-S or DVB-T gateways. Wireless broadband access networks have become possible with the advent of technologies like IEEE 802.11. Our...

This paper presents sequential and parallel derivative-free algorithms for finding a local minimum of smooth and nonsmooth functions of practical interest. It is proved that, under mild assumptions, a sufficient decrease condition holds for a nonsmooth function. Based on this property, the algorithms explore a set of search directions and move to a...

This paper introduces a novel idea for defining a set of orthogonal likely-descent directions to be used with some derivative-free methods that locate the local optimum of a functional, without the computation of derivatives. This paper attempts to capture the essence of useful information (first order information if the function is differentiable)...

This paper proves the existence of an acceleration scheme that introduces a superlinear rate of convergence in the solution of the Convex Inequality Problem CIP by projection techniques. This is accomplished by solving the dual of a quadratic problem that finds the projection of a point on a group of violated and almost violated constraints. This p...

This paper describes a new model for routing in survivable ATM networks and a new parallel projection algorithm for solving the corresponding optimization problem. The proposed algorithm has application in general linear programming (LP). Numerical results for medium size networks are presented and discussed.

This paper formulates an incomplete projection algorithm that is applied to the image recovery problem. The algorithm allows an easy implementation of dynamic load balancing for parallel architectures. Furthermore, the local computation-communication load ratio can be adjusted, since each processor performs a finite number of iterations of any proj...

Input-buffered asynchronous transfer mode (ATM) packet switches are simpler than output-buffered switches. However, due to HOL blocking, their throughput is poor. Neural schedulers represent a promising solution for high throughput input-buffered switching, but their response time variance is too high for realistic hard real-time constraints. To ov...

This paper explores the possibility of including second order information on some derivative-free methods that locate the local optimum of a functional, without the computation of derivatives. We note that a superlinear rate of convergence may be obtained at the expense of extra function evaluations, a feature we try to avoid. This paper attempts t...

The authors analyse a neural scheduler with bounded response time and propose its use in real-time switches

A stochastic neural scheduler is presented which can be used to resolve conflicts in an input-buffered switch. It has smaller mean and variance of response time than neural schedulers recently proposed by Leung [1994, 1998]

Numerical experiments have shown that projection methods are robust for solving the problem of finding a point satisfying a linear system of n variables and m equations; however, their qualities of convergence depend on certain parameters: an n × n symmetric positive definite matrix M, and a vector u with m components. We are concerned here with th...

A stochastic neural scheduler is presented which can he used to resolve conflicts in an input-buffered switch. It has smaller mean and variance of response lime than neural schedulers recently proposed by Leung.

The Convex Inequality Problem (CIP), i.e., find x ∈ ℝn such that Ax = b, g(x) ≤ 0, where A is an p × n matrix, b ∈ ℝm and g(.): ℝn → ℝm is a convex function, has been solved by projection algorithms possessing a linear rate of convergence. We propose a projection algorithm that exhibits global and superlinear rate of convergence under reasonable as...

We present a general scheme for solving the convex feasibility problem and prove its convergence under mild conditions. Unlike previous schemes no exact projections are required. Moreover, we also introduce an acceleration factor, which we denote as the factor, that seems to play a fundamental role to improve the quality of convergence. Numerical t...

We present an algorithm for “approximately” solving a linear system in an inner product space. We find the closest point to the solution belonging to a finite-dimensional space. No algebraic system is directly solved. We generate a sequence of points in the inner product space with the desirable property that the generated sequence is approaching t...

We describe an Armijo-Newton like procedure that locates a feasible point of a non empty system of nonlinear inequalities (and linear equations) in a finite number of operations. Assuming differentiability and Positive Linearly Independence (PLI) of the gradients of the most violated inequalities, the sequence of iterates converges to the relative...

We give an outer approximation algorithm for minimizing a quasi-concave function subject to linear constraints, which possesses certain advantages over related algorithms. It is shown that the algorithm is easily adapted for finding all feasible vertices of a polytope.

A class of methods for solving a large system of convex inequalities is given. All of the methods in the class rely on the technique of solving a large convex system by iteratively solving systems with a smaller number of inequalities. It is shown that the method due to Agmon for solving a system of linear inequalities belongs to this class. The si...

In this paper, we present an application of the Armijo procedure to an algorithm for solving a nonlinear system of equalities and inequalities. The stepsize procedure contained in a quadratically convergent algorithm is replaced by an Armijo procedure on a nondifferentiable function, without any substantial extra computational work and without losi...

A modification of a quadratic algorithm for solving a nonlinear system of mixed equalities and inequalities is proposed. Under suitable conditions, the modified algorithm always generates a local minimum of a function that represents the maximum violation of any equality of inequality of the system. A superlinear rate of convergence is achieved, wh...

A new algorithm is proposed which, under mild assumptions, generates a sequence{x i } that starting at any point inR n will converge to a setX defined by a mixed system of equations and inequalities. Any iteration of the algorithm requires the solution of a linear programming problem with relatively few constraints. By only assuming that the functi...

Strassen's result on the Prokhorov's distance is proved by means of linear programming techniques (the duality theorem). This is a slight modification of Schay's approach (Ann. Probability 2 (1974), 163-166) which, in a sense, is made precise.

A class of algorithms for nonlinearly constrained optimization problems is proposed. The subproblems of the algorithms are linearly constrained quadratic minimization problems which contain an updated estimate of the Hessian of the Lagrangian. Under suitable conditions and updating schemes local convergence and a superlinear rate of convergence are...

In this paper new algorithms for solving linearly constrained optimization problems are proposed. It is shown that certain updating schemes which have been successfully used in unconstrained optimization can also be used to implement these new algorithms. It is proved, that, under suitable conditions the sequence of points generated by the algorith...

El objetivo de esta obra es analizar una serie de técnicas de gran aplicación en el campo de la Ingeniería y la Economía, tales como la optimización de funciones de muestreo, programación cuadrática, programación geométrica, algunos métodos en el área de análisis y diseño de algoritmos de programación no lineal.

Photocopy of typescript. s Thesis (Ph.D.)--University of Wisconsin, 1973. Bibliography: p. 156.

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