Control and Cybernetics on the Implicit Programming Approach in a Class of Mathematical Programs with Equilibrium Constraints * †
نویسندگان
چکیده
In the paper we analyze the influence of implicit programming hypothesis and presence of state constraints on first order optimality conditions to mathematical programs with equilibrium constraints. In the absence of state constraints, we derive sharp stationarity conditions, provided the strong regularity condition holds. In the second part of the paper we suggest an exact penalization of state constraints and test the behavior of standard bundle trust region algorithm on academic examples.
منابع مشابه
Estimation of Concentrations in Chemical Systems at Equilibrium Using Geometric Programming
Geometric programming is a mathematical technique, which has been developed for nonlinear optimization problems. This technique is based on the dual program with linear constraints. Determination of species concentrations in chemical equilibrium conditions is one of its applications in chemistry and chemical engineering fields. In this paper, the principles of geometric programming and its comp...
متن کاملA bundle-free implicit programming approach for a class of elliptic MPECs in function space
Using a standard first-order optimality condition for nonsmooth optimization problems, a general framework for a descent method is developed. This setting is applied to a class of mathematical programs with equilibrium constraints in function space from which a new algorithm is derived. Global convergence of the algorithm is demonstrated in function space and the results are then illustrated by...
متن کاملAn Implicit Programming Approach for a Class of Stochastic Mathematical Programs with Complementarity Constraints
In this paper, we consider a class of stochastic mathematical programs in which the complementarity constraints are subject to random factors and the objective function is the mathematical expectation of a smooth function which depends on both upper and lower level variables and random factors. We investigate the existence, uniqueness, and differentiability of the lower level equilibrium define...
متن کاملA generalized implicit enumeration algorithm for a class of integer nonlinear programming problems
Presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. Also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. The method is easy to u...
متن کاملA revisit of a mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers
In this paper fully fuzzy linear programming (FFLP) problem with both equality and inequality constraints is considered where all the parameters and decision variables are represented by non-negative trapezoidal fuzzy numbers. According to the current approach, the FFLP problem with equality constraints first is converted into a multi–objective linear programming (MOLP) problem with crisp const...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010