Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient conditions, stationary points of the sum of squares of the constraints are feasible points of the MPEC. In usual formulations of MP...

determination a sequence of extracting ore is one of the most important problems in mine annual production scheduling. production scheduling affects mining performance especially in a poly-metallic open pit mine with considering the imposed operational and physical constraints mandated by high levels of reliability in relation to the obtained actual results. one of the important operational con...

Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...

convexity theory and duality theory are important issues in math- ematical programming. within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. finally,...

This paper addresses the globally optimal solution of the network-constrained unit commitment (NCUC) problem incorporating a nonlinear alternating current (AC) model of the transmission network. We formulate the NCUC as a mixed-integer quadratically constrained quadratic programming (MIQCQP) problem. A global optimization algorithm is developed based on a multi-tree approach that iterates betwe...

Abstract— In this paper, a computational method for solving constrained nonlinear optimal control problems is presented with an application to the container crane. The method is based on Banks' et al. iterative approach, in which the nonlinear system state equations are replaced by a sequence of time-varying linear systems. Therefore, The constrained nonlinear optimal control problem can be con...

A numerical algorithm for approximate multi-parametric nonlinear programming is developed. It allows approximate solutions to nonlinear optimization problems to be computed as explicit piecewise linear functions of the problem parameters. In control applications such as nonlinear constrained model predictive control this allows efficient online implementation in terms of an explicit piecewise l...