Computing recession cone of a convex upper image via convex projection

It is possible to solve unbounded convex vector optimization problems (CVOPs) in two phases: (1) computing or approximating the recession cone of the upper image and (2) solving the equivalent bounded CVOP where the ordering cone is extended based on the first phase (Wagner et al., 2023). In this paper, we consider unbounded CVOPs and propose an alternative solution methodology to compute or approximate the recession cone of the upper image. In particular, we relate the dual of the recession cone with the Lagrange dual of weighted sum scalarization problems whenever the dual problem can be written explicitly. Computing this set requires solving a convex (or polyhedral) projection problem. We show that this methodology can be applied to semidefinite, quadratic and linear vector optimization problems and provide some numerical examples

Improved two-phase solution strategy for multiobjective fuzzy stochastic linear programming problems with uncertain probability distribution

Multiobjective Fuzzy Stochastic Linear Programming (MFSLP) problem where the linear inequalities on the probability are fuzzy is called a Multiobjective Fuzzy Stochastic Linear Programming problem with Fuzzy Linear Partial Information on Probability Distribution (MFSLPPFI). The uncertainty presents unique difficulties in constrained optimization problems owing to the presence of conflicting goals and randomness surrounding the data. Most existing solution techniques for MFSLPPFI problems rely heavily on the expectation optimization model, the variance minimization model, the probability maximization model, pessimistic/optimistic values and compromise solution under partial uncertainty of random parameters. Although these approaches recognize the fact that the interval values for probability distribution have important significance, nevertheless they are restricted by the upper and lower limitations of probability distribution and neglected the interior values. This limitation motivated us to search for more efficient strategies for MFSLPPFI which address both the fuzziness of the probability distributions, and the fuzziness and randomness of the parameters. The proposed strategy consists two phases: fuzzy transformation and stochastic transformation. First, ranking function is used to transform the MFSLPPFI to Multiobjective Stochastic Linear Programming Problem with Fuzzy Linear Partial Information on Probability Distribution (MSLPPFI). The problem is then transformed to its corresponding Multiobjective Linear Programming (MLP) problem by using a-cut technique of uncertain probability distribution and linguistic hedges. In addition, Chance Constraint Programming (CCP), and expectation of random coefficients are applied to the constraints and the objectives respectively. Finally, the MLP problem is converted to a single-objective Linear Programming (LP) problem via an Adaptive Arithmetic Average Method (AAAM), and then solved by using simplex method. The algorithm used to obtain the solution requires fewer iterations and faster generation of results compared to existing solutions. Three realistic examples are tested which show that the approach used in this study is efficient in solving the MFSLPPFI

Advances in Optimization and Nonlinear Analysis

The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics

A critical review of the approaches to optimization problems under uncertainty

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Science of Bilkent University, 2001.Thesis (Master's) -- Bilkent University, 2001.Includes bibliographical references leaves 58-72.In this study, the issue of uncertainty in optimization problems is studied. First of all, the meaning and sources of uncertainty are explained and then possible ways of its representation are analyzed. About the modelling process, different approaches as sensitivity analysis, parametric programming, robust optimization, stochastic programming, fuzzy programming, multiobjective programming and imprecise optimization are presented with advantages and disadvantages from different perspectives. Some extensions of the concepts of imprecise optimization are also presented.Gürtuna, FilizM.S

Programmation DC et DCA pour l'optimisation non convexe/optimisation globale en variables mixtes entières (Codes et Applications)

Basés sur les outils théoriques et algorithmiques de la programmation DC et DCA, les travaux de recherche dans cette thèse portent sur les approches locales et globales pour l'optimisation non convexe et l'optimisation globale en variables mixtes entières. La thèse comporte 5 chapitres. Le premier chapitre présente les fondements de la programmation DC et DCA, et techniques de Séparation et Evaluation (B&B) (utilisant la technique de relaxation DC pour le calcul des bornes inférieures de la valeur optimale) pour l'optimisation globale. Y figure aussi des résultats concernant la pénalisation exacte pour la programmation en variables mixtes entières. Le deuxième chapitre est consacré au développement d'une méthode DCA pour la résolution d'une classe NP-difficile des programmes non convexes non linéaires en variables mixtes entières. Ces problèmes d'optimisation non convexe sont tout d'abord reformulées comme des programmes DC via les techniques de pénalisation en programmation DC de manière que les programmes DC résultants soient efficacement résolus par DCA et B&B bien adaptés. Comme première application en optimisation financière, nous avons modélisé le problème de gestion de portefeuille sous le coût de transaction concave et appliqué DCA et B&B à sa résolution. Dans le chapitre suivant nous étudions la modélisation du problème de minimisation du coût de transaction non convexe discontinu en gestion de portefeuille sous deux formes : la première est un programme DC obtenu en approximant la fonction objectif du problème original par une fonction DC polyèdrale et la deuxième est un programme DC mixte 0-1 équivalent. Et nous présentons DCA, B&B, et l'algorithme combiné DCA-B&B pour leur résolution. Le chapitre 4 étudie la résolution exacte du problème multi-objectif en variables mixtes binaires et présente deux applications concrètes de la méthode proposée. Nous nous intéressons dans le dernier chapitre à ces deux problématiques challenging : le problème de moindres carrés linéaires en variables entières bornées et celui de factorisation en matrices non négatives (Nonnegative Matrix Factorization (NMF)). La méthode NMF est particulièrement importante de par ses nombreuses et diverses applications tandis que les applications importantes du premier se trouvent en télécommunication. Les simulations numériques montrent la robustesse, rapidité (donc scalabilité), performance et la globalité de DCA par rapport aux méthodes existantes.Based on theoretical and algorithmic tools of DC programming and DCA, the research in this thesis focus on the local and global approaches for non convex optimization and global mixed integer optimization. The thesis consists of 5 chapters. The first chapter presents fundamentals of DC programming and DCA, and techniques of Branch and Bound method (B&B) for global optimization (using the DC relaxation technique for calculating lower bounds of the optimal value). It shall include results concerning the exact penalty technique in mixed integer programming. The second chapter is devoted of a DCA method for solving a class of NP-hard nonconvex nonlinear mixed integer programs. These nonconvex problems are firstly reformulated as DC programs via penalty techniques in DC programming so that the resulting DC programs are effectively solved by DCA and B&B well adapted. As a first application in financial optimization, we modeled the problem pf portfolio selection under concave transaction costs and applied DCA and B&B to its solutions. In the next chapter we study the modeling of the problem of minimization of nonconvex discontinuous transaction costs in portfolio selection in two forms: the first is a DC program obtained by approximating the objective function of the original problem by a DC polyhedral function and the second is an equivalent mixed 0-1 DC program. And we present DCA, B&B algorithm, and a combined DCA-B&B algorithm for their solutions. Chapter 4 studied the exact solution for the multi-objective mixed zero-one linear programming problem and presents two practical applications of proposed method. We are interested int the last chapter two challenging problems: the linear integer least squares problem and the Nonnegative Mattrix Factorization problem (NMF). The NMF method is particularly important because of its many various applications of the first are in telecommunications. The numerical simulations show the robustness, speed (thus scalability), performance, and the globality of DCA in comparison to existent methods.ROUEN-INSA Madrillet (765752301) / SudocSudocFranceF

Large-Scale Modelling and Interactive Decision Analysis

These Proceedings report the scientific results of an International Workshop attended by more than fifty scientists from thirteen countries. This volume is structured in three parts: (I) Theory and Methodology, (II) Interaction Principles and Computational Aspects and (III) Applications. Part I contains papers dealing with utility and game theory, multicriteria optimizations theory and interactive procedures, dynamic models/systems and concepts of multicriteria analysis. Papers dealing with the user-machine interface, intelligent (user-friendly) decision support and problems of computational aspects are included in Part II. Contributions with applications are mainly concentrated in Part III but can also be found in several papers in other parts. Use of the term "large-scale" in the title of the Proceedings was especially substantiated by contributions dealing with modelling and decision analysis problems of the size of a whole national economy like structuring the carbochemical industry, the energy system or even natural gas trade in Europe

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

Aspiration Based Decision Support Systems

This book focuses the methodology of decision analysis and support related to the principle of reference point optimization (developed by the editors of this volume and called also variously: aspiration-led decision support, quasi-satisfying framework of rationality, DIDAS methodology etc.). The selection principle applied for this volume was to concentrate on advances of theory and methodology, related to the focusing theme, to supplement them by experiences and methodological advances gained through wide applications and tests in one particular application area - the programming of development of industrial structures in chemical industry, and finally to give a very short description of various software products developed in the contracted study agreement