Coupling the Auxiliary Problem Principle with Descent Methods of Pseudoconvex Programming
نویسنده
چکیده
The descent auxiliary problem method allows one to nd the solution of minimization problems by solving a sequence of auxiliary problems which incorporate a linesearch strategy. We derive the basic algorithm and study its convergence properties within the framework of innnite dimensional pseudoconvex minimization. We also introduce a partial descent type auxiliary problem method which partially linearizes the objective functional and includes the auxiliary term only for of subset of variables. Numerous examples of this very general scheme are provided.
منابع مشابه
Pseudoconvex Multiobjective Continuous-time Problems and Vector Variational Inequalities
In this paper, the concept of pseudoconvexity and quasiconvexity for continuous~-time functions are studied and an equivalence condition for pseudoconvexity is obtained. Moreover, under pseudoconvexity assumptions, some relationships between Minty and Stampacchia vector variational inequalities and continuous-time programming problems are presented. Finally, some characterizations of the soluti...
متن کاملPosynomial geometric programming problem subject to max–product fuzzy relation equations
In this article, we study a class of posynomial geometric programming problem (PGPF), with the purpose of minimizing a posynomial subject to fuzzy relational equations with max–product composition. With the help of auxiliary variables, it is converted convert the PGPF into an equivalent programming problem whose objective function is a non-decreasing function with an auxiliary variable. Some pr...
متن کاملOptimality and Duality for an Efficient Solution of Multiobjective Nonlinear Fractional Programming Problem Involving Semilocally Convex Functions
In this paper, the problem under consideration is multiobjective non-linear fractional programming problem involving semilocally convex and related functions. We have discussed the interrelation between the solution sets involving properly efficient solutions of multiobjective fractional programming and corresponding scalar fractional programming problem. Necessary and sufficient optimality...
متن کاملA Free Line Search Steepest Descent Method for Solving Unconstrained Optimization Problems
In this paper, we solve unconstrained optimization problem using a free line search steepest descent method. First, we propose a double parameter scaled quasi Newton formula for calculating an approximation of the Hessian matrix. The approximation obtained from this formula is a positive definite matrix that is satisfied in the standard secant relation. We also show that the largest eigen value...
متن کاملAn interval-valued programming approach to matrix games with payoffs of triangular intuitionistic fuzzy numbers
The purpose of this paper is to develop a methodology for solving a new type of matrix games in which payoffs are expressed with triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, the concept of solutions for matrix games with payoffs of TIFNs is introduced. A pair of auxiliary intuitionistic fuzzy programming models for players are established to determine optimal strategies...
متن کامل