Objective of this article is to study the conditions for existence efficient solution interval optimization problem with inequality constraints. Here active constraints are considered in inclusion form. The regularity condition Karush–Kuhn–Tucker point derived. This depends on interval-valued gradient function These new concepts literature optimization. gH-differentiability used theoretical dev...

In this paper, we study the nonconvex nonsmooth optimization problem (P) of minimizing a tangentially convex function with inequality constraints where constraint functions are convex. This is done by using cone tangential subdifferentials together new qualification. Indeed, present qualification to guarantee that Karush-Kuhn-Tucker conditions necessary and sufficient for optimality (P). Moreov...

Abstract In this paper, we introduce a new concept of sets and class functions called E -univex functions, respectively. For an -differentiable function, the -univexity is introduced by generalizing several concepts generalized convexity earlier defined into optimization theory. addition, some properties are investigated. Further, also introduced. Then, sufficiency so-called -Karush–Kuhn–Tucker...

This paper is concerned with the Lipschitzian behavior of the optimal set of convex semi-infinite optimization problems under continuous perturbations of the right hand side of the constraints and linear perturbations of the objective function. In this framework we provide a sufficient condition for the metric regularity of the inverse of the optimal set mapping. This condition consists of the ...

In this paper preconditioners for linear systems arising in interior–point methods for the solution of distributed control problems are derived and analyzed. The matrices K in these systems have a block structure with blocks obtained from the discretization of the objective function and the governing differential equation. The preconditioners have a block structure with blocks being composed of...

Abstract In this paper, a class of directionally differentiable multiobjective programming problems with inequality, equality and vanishing constraints is considered. Under both the Abadie constraint qualification modified qualification, Karush–Kuhn–Tucker type necessary optimality conditions are established for such nondifferentiable vector optimization by using nonlinear version Gordan theore...

In this paper, the Fischer–Burmeister active-set trust-region (FBACTR) algorithm is introduced to solve nonlinear bilevel programming problems. FBACTR algorithm, a Karush–Kuhn–Tucker (KKT) condition used with function transform (NBLP) problem into an equivalent smooth single objective problem. To ensure global convergence for strategy globalization strategy. The theory of presented. clarify eff...

Convex optimization solvers are widely used in the embedded systems that require sophisticated algorithms including model predictive control (MPC). In this paper, we aim to reduce online solve time of such convex so as total runtime algorithm and make it suitable for real-time optimization. We exploit property Karush–Kuhn–Tucker (KKT) matrix involved solution problem only some parts change duri...

Train energy saving problem investigates how to control train's velocity such that the quantity of energy consumption is minimized and some system constraints are satis ed. On the assumption that the train's weights on different links are estimated by fuzzy variables when making the train scheduling strategy, we study the fuzzy train energy saving problem. First, we propose a fuzzy energy ...