The approximate Karush-Kuhn-Tucker (AKKT) condition is introduced being a necessary of the local weak efficient solution for optimistic bilevel optimization problems with multiple objectives in upper-level problems. We transform multi-objective problem into single-level by means value function transformation or KKT transformation. then prove that AKKT point to be without any constraint qualific...

In this paper, we consider a nonsmooth multiobjective semi-infinite programming problem with vanishing constraints (MOSIPVC). We introduce stationary conditions for the MOSIPVCs and establish the strong Karush-Kuhn-Tucker type sufficient optimality conditions for the MOSIPVC under generalized convexity assumptions.

In this paper we characterize the local maxima of a continuous global optimization formulation for finding the independence number of a graph. Classical Karush-Kuhn-Tucker conditions and simple combinatorial arguments are found sufficient to deduce several interesting properties of the local and global maxima. These properties can be utilized in developing new approaches to the maximum independ...

The paper presents a reformulation of the Karush-KuhnTucker (KKT) system associated nonlinear programming problem into an equivalent system of smooth equations. Classical Newton method is applied to solve the system of equations. The superlinear convergence of the primal sequence, generated by proposed method, is proved. The preliminary numerical results with a problems test set are presented.

Abstract-A second-order dual to a nonlinear programming problem is formulated. This dual uses the Ritz John necessary optimality conditions instead of the Karush-Kuhn-Tucker necessary optimal&y conditions, and thus, does not require a constraint qualification. Weak, strong, strictconverse, and converse duality theorems between primal and dual problems are established. @ 2001 Elsevier Science Lt...

The author regrets that some terms are missing or misspecified in the Karush–Kuhn–Tucker conditions in Sections 3.7–3.10 on page 346. Corrections are given below. add multiplier p m c m (discount rate in tree node m multiplied by the probability of its occurrence) to d d (number of days in demand season d).

The purpose of this paper is to characterize the weak Pareto optimality for multiobjective pseudoconvex problem. In fact, it is a first order optimality characterization that generalize the Karush-Kuhn-Tucker condition. Moreover, this work is an extension of the single-objective case [6] to the multiobjective one with pseudoconvex continuous functions. Mathematics Subject Classification: 46N10,...

In 1948, Duggan and Luck (1) observed that certain organic anions in appropriate concentrations prevented the rise in viscosity of bovine serum albumin caused by 6 M urea. Among the anions studied, dodecyl sulfate was found to be the most effective. In 1957, Markus and Karush (2) showed that the rise in levorotation of human serum albumin caused by 6 M urea could also be prevented or reversed b...