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...

We consider a class of constrained optimization problems where the objective function is a sum of a smooth function and a nonconvex non-Lipschitz function. Many problems in sparse portfolio selection, edge preserving image restoration and signal processing can be modelled in this form. First we propose the concept of the Karush-Kuhn-Tucker (KKT) stationary condition for the non-Lipschitz proble...

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...

This article is concerned with a general scheme on how to obtain constructive proofs for combinatorial theorems that have topological proofs so far. To this end the combinatorial concept of Tucker-property of a finite group G is introduced and its relation to the topological Borsuk-Ulam-property is discussed. Applications of the Tucker-property in combinatorics are demonstrated.

Entropy functionals (i.e. convex integral functionals) and extensions of these functionals are minimized on convex sets. This paper is aimed at reducing as much as possible the assumptions on the constraint set. Dual equalities and characterizations of the minimizers are obtained with weak constraint qualifications.

In this paper, we consider a class of structured nonsmooth difference-of-convex (DC) constrained DC programs in which the first convex component objective and constraints is sum smooth function, their second supremum finitely many functions. The existing methods for problem usually have weak convergence guarantee or require feasible initial point. Inspired by recent work Pang et al. [Pang J-S, ...

In this paper, we consider the width invariant trapezoidal and triangularapproximations of fuzzy numbers. The presented methods avoid the effortful computation of Karush-Kuhn-Tucker Theorem. Some properties of the new approximation methods are presented and the applicability of the methods is illustrated by examples. In addition, we show that the proposed approximations of fuzzy numbers preserv...

The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance which for numerous theoretical, algorithmic, applied issues operations research difficult overstate. underlying theme our systematical replacement conventional metric regularity related requirements by much weaker subregulatity ones that lead us significantly stronger comple...

In this note we present a multigrid preconditioning method for solving quadratic optimization problems constrained by fractional diffusion equation. Multigrid methods within the all-at-once approach to solve first order optimality Karush–Kuhn–Tucker (KKT) systems are widely popular, but their development have relied on underlying being sparse. On other hand, most discretizations, matrix represe...