El Mostafa Kalmoun

• PhD & HdR
• Al Akhawayn University

We present a unified numerical method to determine the shapes of multiple Hele-Shaw bubbles in steady motion, and in the absence of surface tension, in three planar domains: free space, the upper half-plane, and an infinite channel. Our approach is based on solving the free boundary problem for the bubble boundaries using a fast and accurate bounda...

The KKT reformulation is widely recognized as a prominent approach for analyzing bilevel optimization problems, especially in the case of convex lower-level problems. This paper focuses on exploring the KKT reformulation and deriving second-order necessary optimality conditions for local solutions to bilevel programs. The derived optimality conditi...

We investigate the so-called nonsmooth bilevel semi-infinite programming problem when the involved functions are nonconvex. This type of problems consists of an infinite number of constraints with arbitrary index sets. To establish the optimality conditions, we rewrite upper estimates of three recently developed subdifferentials of the value functi...

Pumpkin is a vital crop cultivated globally, and its productivity is crucial for food security, especially in developing regions. Accurate and timely detection of pumpkin leaf diseases is essential to mitigate significant losses in yield and quality. Traditional methods of disease identification rely heavily on subjective judgment by farmers or exp...

The purpose of this paper is to derive primal and dual second-order necessary optimality conditions for a standard bilevel optimization problem with both smooth and nonsmooth data. The approach involves utilizing two different reformulations of the hierarchical model as a single-level problem under a partial calmness assumption. The first reformula...

In the original paper [...]

A multiobjective generalized Nash equilibrium problem (MGNEP) is a Nash equilibrium problem with constraints that include multiobjective games. We focus in this paper on examining the approximate Karush–Kuhn–Tucker (KKT) conditions for MGNEPs and their impact on the global convergence of algorithms. To begin, we define standard approximate weak KKT...

We establish Pontryagin optimality conditions for a generalized bilevel optimal control problem in which the leader is subject to a pure state inequality constraint, while the follower is governed by a non-convex quasi-variational inequality parameterized by the final state. To simplify the problem at hand, we convert it into a single-level optimal...

We consider a nonsmooth and nonconvex mathematical program with equilibrium constraints (MPEC) where its functions are not necessarily locally Lipschitz/continuous. In exploiting the idea of directional convexificators introduced by Dempe and Pelicka [Necessary optimality conditions for optimistic bilevel programming problems using set-valued progr...

We present in this paper a numerical solution of a generalized diffusion-based image denoising model, using the finite element computing platform FEniCS. The generalized model contains as special cases three classical denoising techniques: linear isotropic diffusion, total variation, and Perona-Malik method. The numerical simulation using four clas...

In this paper, we establish optimality conditions for a nonsmooth multiobjective semi-infinite programming problem subject to switching constraints. In particular, we employ a surrogate problem and a suitable constraint qualification to state necessary M-stationary conditions in terms of Clarke sub-differentials. Moreover, we demonstrate that in di...

Let Ω be the multiply connected domain in the extended complex plane \(\overline {\mathbb {C}}\) obtained by removing m non-overlapping rectilinear segments from the infinite strip \(S=\{z : \left |\text {Im} z\right |<\pi /2\}\). In this paper, we present an iterative method for numerical computation of a conformally equivalent bounded multiply co...

We investigate optimality conditions for a nonsmooth multiobjective semi-infinite programming problem subject to switching constraints. In particular, we employ a surrogate problem and a suitable constraint qualification to state necessary M-stationary conditions in terms of tangential subdifferentials. An example is given at the end to illustrate...

We take up a nonsmooth multiobjective optimization problem with tangentially convex objective and constraint functions. In employing a suitable constraint qualification, we formulate both necessary and sufficient optimality conditions for (local) quasi efficient solutions in terms of tangential subdifferentials. Furthermore, under generalized conve...

A numerical simulation of the thermal properties is conducted for an isotropic and homogeneous infinite strip composite reinforced by carbon nanotubes (CNTs) and containing voids. The CNTs can be uniformly or randomly distributed but are non-overlapping. We model the CNTs as thin perfectly conducting elliptic inclusions and assume the voids to be o...

It was recently reported that harmonic inpainting or Laplace interpolation when used in the context of image compression can yield impressive reconstruction results if the encoded pixels were carefully selected. Mathematically, the problem translates into a mixed Dirichlet–Neumann boundary value problem with Dirichlet data coming from the known obs...

Let $S$ be a strip in ${\mathbb{C}}$ and let $E\subset S$ be a union of disjoint segments. For the domain $S \setminus E$, we construct a numerical conformal mapping onto a domain bordered by smooth Jordan curves. To this aim, we use the boundary integral equation method from [19]. In particular, we apply this method to study the conformal capacity...

The main required organ of the biological system is the Central Nervous System (CNS), which can influence the other basic organs in the human body. The basic elements of this important organ are neurons, synapses, and glias (such as astrocytes, which are the highest percentage of glias in the human brain). Investigating, modeling, simulation, and h...

We consider the steady heat conduction problem within a thermal isotropic and homogeneous infinite strip composite reinforced by uniformly and randomly distributed non-overlapping carbon nanotubes (CNTs) and containing voids. We treat the CNTs as thin perfectly conducting elliptic inclusions and assume the voids to be of circular shape and act as b...

In combining the value function approach and tangential subdifferentials, we establish necessary optimality conditions of a nonsmooth multiobjective bilevel programming problem under a suitable constraint qualification. The upper level objectives and constraint functions are neither assumed to be necessarily locally Lipschitz nor convex.

Scale deposits can reduce equipment efficiency in the oil and petrochemical industry. The gamma attenuation technique can be used as a non-invasive effective tool for detecting scale deposits in petroleum pipelines. The goal of this study is to propose a dual-energy gamma attenuation method with radial basis function neural network (RBFNN) to deter...

To the best knowledge of the authors, in former studies in the field of measuring volume fraction of gas, oil, and water components in a three-phase flow using gamma radiation technique, the existence of a scale layer has not been considered. The formed scale layer usually has a higher density in comparison to the fluid flow inside the oil pipeline...

Two phase flows are of particular importance in various research fields. In the current article, a novel system consists of an X-ray tube and one sodium iodide crystal detector with ability of determining type of flow regime as well as void fraction percentage of a two phase flow, is proposed. MCNP-X code was used for physical modelling of the prop...

Radiation-based instruments have been widely used in petrochemical and oil industries to monitor liquid products transported through the same pipeline. Different radioactive gamma-ray emitter sources are typically used as radiation generators in the instruments mentioned above. The idea at the basis of this research is to investigate the use of an...

In this paper, the feasibility of using an X-ray tube instead of radioisotope sources for measuring volume fractions of gas, oil, and water in two typical flow regimes of three-phase flows, namely, annular and stratified, is evaluated. This study’s proposed detection system is composed of an X-ray tube, a 1 inch × 1 inch NaI detector, and one Pyrex...

The main objective of the present research is to combine the effect of scale thickness on the flow pattern and characteristics of two-phase flow that is used in oil industry. In this regard, an intelligent nondestructive technique based on combination of gamma radiation attenuation and artificial intelligence is proposed to determine the type of fl...

We study a unified form of Tikhonov regularization for ill-posed problems with a general data similarity term. We discuss sufficient conditions on this generalized Tikhonov functional that guarantee existence and stability of solutions. Furthermore, we show that some particular cases of similarity functionals and regularization techniques can be ca...

We consider a nonsmooth semi-infinite interval-valued vector programming problem, where the objectives and constraints functions need not to be locally Lipschitz. Using Abadie's constraint qualification and convexificators, we provide Karush-Kuhn-Tucker necessary optimality conditions by converting the initial problem into a bi-criteria optimizatio...

In this work, we demonstrate the connection between the solutions of approximate vector variational inequalities and approximate efficient solutions of corresponding nonsmooth vector optimization problems via generalized approximate invex functions. The underlying variational inequalities are stated under the Clarke’s generalized Jacobian.

This note corrects an error in our paper RAIRO-Operations Research /doi.org/10.1051/ro/2020066 as we should drop the expression ”with at least one strict inequality” in the definition of interval order in Section 2. Instead of proposing this short amendment, the authors of RAIRO-Operations Research doi.org/10.1051/ro/2020107 gave a proposition that...

We consider Mityuk's function and radius which have been proposed in [17] as generalizations of the reduced modulus and conformal radius to the cases of multiply connected domains. We present a numerical method to compute Mityuk's function and radius for canonical domains that consist of the unit disk with circular/radial slits. Our method is based...

We study the motion of a single point vortex in simply- and multiply-connected polygonal domains. In the case of multiply-connected domains, the polygonal obstacles can be viewed as the cross-sections of 3D polygonal cylinders. First, we utilize conformal mappings to transfer the polygonal domains onto circular domains. Then, we employ the Schottky...

We are interested in local quasi efficient solutions for nonsmooth vector optimization problems under new generalized approximate invexity assumptions. We formulate necessary and sufficient optimality conditions based on Stampacchia and Minty types of vector variational inequalities involving Clarke’s generalized Jacobians. We also establish the re...

We consider the steady heat conduction problem within a thermal isotropic and homogeneous square ring composite reinforced by nonoverlapping and randomly distributed carbon nanotubes (CNTs). We treat the CNTs as rigid line inclusions and assume their temperature distribution to be fixed to an undetermined constant value along each line. We suppose...

Interval-valued functions have been widely used to accommodate data inexactness in optimization and decision theory. In this paper, we study interval-valued vector optimization problems, and derive their relationships to interval variational inequality problems, of both Stampacchia and Minty types. Using the concept of interval approximate convexit...

We study the motion of a single point vortex in simply and multiply connected polygonal domains. In case of multiply connected domains, the polygonal obstacles can be viewed as the cross-sections of 3D polygonal cylinders. First, we utilize conformal mappings to transfer the polygonal domains onto circular domains. Then, we employ the Schottky-Klei...

Tikhonov regularization and total variation (TV) are two famous smoothing techniques used in variational image processing problems and in particular for optical flow computation. We consider a new method that combines these two approaches in order to reconstruct piecewise-smooth optical flow. More precisely, we split the flow vector into the sum of...

We are interested in local quasi efficient solutions for nonsmooth vector optimization problems under new generalized approximate invexity assumptions. We formulate necessary and sufficient optimality conditions based on Stampacchia and Minty types of vector variational inequalities involving Clarke's generalized Jacobians. We also establish the re...

We consider the steady heat conduction problem within a thermal isotropic and homogeneous square ring composite reinforced by non-overlapping and randomly distributed carbon nanotubes (CNTs). We treat the CNTs as rigid line inclusions and assume their temperature distribution to be fixed to an undetermined constant value along each line. We suppose...

We consider Mityuk's function and radius which have been proposed in \cite{Mit} as generalizations of the reduced modulus and conformal radius to the cases of multiply connected domains. We present a numerical method to compute Mityuk's function and radius for canonical domains that consist of the unit disk with circular/radial slits. Our method is...

Total variation (TV) is widely used in many image processing problems including the regularization of optical flow estimation. In order to deal with non differentiability of the TV regularization term, smooth approximations have been considered in the literature. In this paper, we investigate the use of three known smooth TV approximations, namely:...

We describe the implementation details and give the experimental results of three optimization algorithms for dense optical flow computation. In particular, using a line search strategy, we evaluate the performance of the unilevel truncated Newton method (LSTN), a multireso-lution truncated Newton (MR/LSTN) and a full multigrid truncated Newton (FM...

We consider the numerical treatment of the optical flow problem by evaluating the performance of the trust region method versus the line search method. To the best of our knowledge, the trust region method is studied here for the first time for variational optical flow computation. Four different optical flow models are used to test the performance...

The aim of this paper is to construct a method for developing a triad design on vv objects TD(v)TD(v), for the general case v=6n+1v=6n+1. This method depends on analyzing the triples to construct a starter for TD(v)TD(v), denoted by STD(v)STD(v), using interval techniques of the triples in the starter. We illustrate this construction by considering...

This monograph offers design for fast and reliable technique in the dense motion estimation. This Multilevel Optimization for Dense Motion Estimation work blends both theory and applications to equip reader with an understanding of basic concepts necessary to apply in solving dense motion in a sequence of images. Illustrating well-known variation m...

We introduce the use of optimization-based multigrid techniques for dense optical flow computation. In particular, we evaluate the performance of a multigrid optimization (MG/OPT) algorithm based on a line search strategy for large-scale optimization like truncated Newton. Our experimental tests have shown that the algorithm outperforms the truncat...

Triad design is a class of designs introduced by H. Ibrahim and W. D. Wallis [J. Combin. Inform. Syst. Sci. 30, 5–17 (2005)], for arranging the v 3 distinct triples that satisfy several properties. The purpose of this paper is to present algorithms for constructing new triad designs for v=7,11,13,17,19 and 23. We make use of the idea of difference...

We evaluate the performance of different optimization techniques developed in the context of optical flow computation with different variational models. In particular, based on truncated Newton (TN) methods that have been an effective approach for large-scale unconstrained optimization, we develop the use of efficient multilevel schemes for computi...

Motivated by recent applications to 3D medical motion estimation, we consider the problem of 3D optical flow computation in real time. The 3D optical flow model is derived from a straightforward extension of the 2D Horn–Schunck model and discretized using standard finite differences. We compare memory costs and convergence rates of four numerical s...

Summary form only given. Optical flow computation is known to be a fundamental step in many applications in image processing, pattern recognition, data compression, and biomedical technology. The goal is to compute an approximation to the projection of the 3D motion field onto the imaging surface. I consider in this talk the problem of real-time co...

This paper deals with parallel 2D and 3D V-cycle multigrid implementation for computing the optical flow between two images. We compare memory costs and convergence rates of four schemes: the Horn-Schunck algorithm (Gauss-Seidel) and multigrid with three different strategies of coarse grid operators discretization: direct coarsening, lumping and Ga...

Some new KKM theorems are first presented for transfer closed-valued maps in both topological vector spaces and topo-logical spaces with no linear structure, namely G-convex spaces. Applications are then given to establish the existence for vector equilibrium problems, mixed variational inequalities, greatest elements for a binary relation, and Fan...

This paper is concerned with existence theorems for cone-saddle points of vector-valued functions in finite dimensional Euclidean spaces. By means of vector variational-like inequalities, we first characterize a vector saddle point problem and obtain the existence result under some conditions on the subdifferentiable of the vector-valued function....

In this paper, some generalized concepts about semicontinuity and convexity for vector-valued bifunctions are introduced. A new existence theorem for vector equilibrium problems is proved. Further, a random version of this result is considered. Applications to cone saddle points, random vector optimization, random vector variational inequalities, a...

In this paper, we research existence theorems of saddle points for vector valued function and broadly classfy into two categories. One of those classes has been investigated from the beginning of studying about this field and is besed on some fixed point theorems or scalar minimax theorems and are researched by Nieuwenhuis, Ferro, Tanaka and so on....

We focus our attention on generalized vector equilibrium problems. In particular, we formulate a general and unified existence theorem, present an analysis for the assumptions used in this result, and give some applications to vector variational inequalities, vector complementarity problems and vector optimization.

We focus our attention on generalized vector equilibrium problems. In particular, we formulate a general and unified existence theorem, present an analysis for the assumptions used in this result, and give some applications to vector variational inequalities, vector complementarity problems and vector optimization.

In the present paper, slightly modifying the topological KKM Theorem of Park and Kim (1996), we obtain a new existence theorem for generalized vector equilibrium problems related to an admissible multifunction. We work here under the general framework of G-convex space which does not have any linear structure. Also, we give applications to greatest...

In this note, we present a generalization of the Ky Fan's minimax inequality theorem by means of a new version of the KKM lemma. Application is then given to establish existence of solutions for mixed equilibrium problems. Finally, we investigate the relationship between the latter problems and hemivariational inequalities.

We establish some facts about vector equilibrium problems, which are models that may be used as a unified and natural extension of many problems in modern analysis. First, we present several formulations and compare them. Then we single out some special cases and discuss the techniques and assumptions used for the existence theory. Finally, we give...