Introduction The first part of the paper presents several properties of saddle point matrices with two vector blocks. In these block matrices, the top-left block is a real square matrix , the topright block is the column vector with all entries , the bottom-left block is transposed, and the bottom-right block has the single entry . If is symmetric, the saddle point matrix can be interpreted as ...

A few Karush-Kuhn-Tucker type of sufficient optimality conditions are given in this paper for nonsmooth continuous-time nonlinear multi-objective optimization problems in the Banach space L∞ [0, T ] of all n-dimensional vector-valued Lebesgue measurable functions which are essentially bounded, using Clarke regularity and generalized convexity. Further, we establish duality theorems for Wolfe an...

We consider the problem of correcting an inconsistent system of linear inequalities, Ax ≤ b, subject to nonnegativity constraints, x ≥ 0. We formulate this problem as a nonlinear program and derive the corresponding Karush-Kuhn-Tucker conditions. These conditions reveal several interesting properties that solutions must satisfy and allow us to derive several equivalent problems that involve few...

This paper is devoted to studying the robust isolated calmness of the Karush– Kuhn–Tucker (KKT) solution mapping for a large class of interesting conic programming problems (including most commonly known ones arising from applications) at a locally optimal solution. Under the Robinson constraint qualification, we show that the KKT solution mapping is robustly isolated calm if and only if both t...

We report on the use of a quadratic programming technique in recent and upcoming spectrum auctions in Europe. Specifically, we compute a unique point in the core that minimizes the sum of squared deviations from a reference point, for example, from the Vickrey-Clarke-Groves payments. Analyzing the Karush-Kuhn-Tucker conditions, we demonstrate that the resulting payments can be decomposed into a...

Abstract This paper deals with a robust multiobjective optimization problem involving nonsmooth/nonconvex real-valued functions. Under an appropriate constraint qualification, we establish necessary optimality conditions for weakly efficient solutions of the considered problem. These are presented in terms Karush-Kuhn-Tucker multipliers and convexificators related Examples illustrating our find...

where (a) because that E and Tr are both linear operators and Tr[E[ZZ ]] is certain positive number which is independent on the optimization variables, then this term can be replaced by another positive constant Tr[EZ[Z ]EZ[Z]]. Based on the equivalence between (13) and (14), we can apply the result shown in [28, Lemma 2]. Since the constraint set is polyhedral in the formulation (3), the linea...

The Karush–Kuhn–Tucker (KKT) optimality conditions and saddle point optimality conditions in fuzzy programming problems have been studied in literature by various authors under different conditions. In this paper, by considering a partial order relation on the set of fuzzy numbers, and convexity with differentiability of fuzzy mappings, we have obtained the Fritz John (FJ) constraint qualificat...

This paper investigates bandwidth allocation and scheduling of networked control systems (NCSs) with nonlinear-programming techniques. The bandwidth utilization (BU) is defined in terms of sampling frequency. An exponential and a quadratic approximation are formulated to describe system performance versus the sampling frequencies. The optimal sampling frequencies are obtained by solving the app...

The EM-ML (expectation-maximization, maximum-likelihood) algorithm for PET reconstruction is an iterative method. Sequence convergence to a fixed point that satisfies the Karush-Kuhn-Tucker conditions for optimality has previously been established [1, 2, 3]. This correspondence first gives an alternative proof of sequence convergence and optimality based on direct expansion of certain Kullback ...