We consider the application of the globalized semismooth Newton method to the solution of (the KKT conditions of) quasi variational inequalities. We show that the method is globally and locally superlinearly convergent for some important classes of quasi variational inequality problems. We report numerical results to illustrate the practical behavior of the method.

Homogeneous programming is an important class of optimization problems. The purpose of this note is to give a truly equivalent characterization of KKT-points of homogeneous programming problems, which corrects a result given by Lasserre and Hiriart-Urruty in Ref. 9.

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.

This article points out an important source of inefficiency in Platt’s sequential minimal optimization (SMO) algorithm that is caused by the use of a single threshold value. Using clues from the KKT conditions for the dual problem, two threshold parameters are employed to derive modifications of SMO. These modified algorithms perform significantly faster than the original SMO on all benchmark d...

A new optimality condition for minimization with general constraints is introduced. Unlike the KKT conditions, this condition is satissed by local minimizers of nonlinear programming problems, independently of constraint qualiications. The new condition implies, and is strictly stronger than, Fritz-John optimality conditions. Suu-ciency for convex programming is proved.

The support vector machine (SVM) is a powerful and widely used classification algorithm. This paper uses the Karush-Kuhn-Tucker conditions to provide rigorous mathematical proof for new insights into behavior of SVM. These perhaps unexpected relationships between SVM two other linear classifiers: mean difference maximal data piling direction. For example, we show that in many cases can be viewe...

The lecture presents an integrated modeling and solution framework aiming at the robust and efficient solution of very large instances of tree-sparse programs. This wide class of nonlinear programs (NLP) is characterized by an underlying tree topology. It includes, in particular, dynamic stochastic programs in scenario tree formulation, multistage stochastic programs, where the objective and co...