A solving tool for fuzzy quadratic optimal control problems

In this paper we propose an iterative method to solve an optimal control problem, with fuzzy target and constraints. The algorithm is developed in such a way as to satisfy the target function and the constraints. The algorithm can be applied only if a method exists to solve a crisp parametric sub-problem obtained by the original one. This is the case for a quadratic-linear target function with linear constraints, for which some well established solvable methods exist for the crisp associated sub-problem. A numerical test confirmed the good convergence properties.fuzzy, mathematical programming

New optimality conditions for multiobjective fuzzy programming problems

In this paper we study fuzzy multiobjective optimization problems de ned for n variables. Based on a new p-dimensional fuzzy stationary-point de nition, necessary e ciency conditions are obtained. And we prove that these conditions are also su cient under new fuzzy generalized convexity notions. Furthermore, the results are obtained under general di erentiability hypothesis.The research in this paper has been supported by Fondecyt-Chile, project 1151154 and by Ministerio de Economía y Competitividad, Spain, through grant MINECO/FEDER(UE) MTM2015-66185-P

Domination and Decomposition in Multiobjective Programming

During the last few decades, multiobjective programming has received much attention for both its numerous theoretical advances as well as its continued success in modeling and solving real-life decision problems in business and engineering. In extension of the traditionally adopted concept of Pareto optimality, this research investigates the more general notion of domination and establishes various theoretical results that lead to new optimization methods and support decision making. After a preparatory discussion of some preliminaries and a review of the relevant literature, several new findings are presented that characterize the nondominated set of a general vector optimization problem for which the underlying domination structure is defined in terms of different cones. Using concepts from linear algebra and convex analysis, a well known result relating nondominated points for polyhedral cones with Pareto solutions is generalized to nonpolyhedral cones that are induced by positively homogeneous functions, and to translated polyhedral cones that are used to describe a notion of approximate nondominance. Pareto-oriented scalarization methods are modified and several new solution approaches are proposed for these two classes of cones. In addition, necessary and sufficient conditions for nondominance with respect to a variable domination cone are developed, and some more specific results for the case of Bishop-Phelps cones are derived. Based on the above findings, a decomposition framework is proposed for the solution of multi-scenario and large-scale multiobjective programs and analyzed in terms of the efficiency relationships between the original and the decomposed subproblems. Using the concept of approximate nondominance, an interactive decision making procedure is formulated to coordinate tradeoffs between these subproblems and applied to selected problems from portfolio optimization and engineering design. Some introductory remarks and concluding comments together with ideas and research directions for possible future work complete this dissertation

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