In this paper we consider a mathematical program with second-order cone complementarity constraints (SOCMPCC). The SOCMPCC generalizes the mathematical program with complementarity constraints (MPCC) in replacing the set of nonnegative reals by second-order cones. There are difficulties in applying the classical Karush–Kuhn–Tucker (KKT) condition to the SOCMPCC directly since the usual constrai...

Mathematics (ABSTRACT) This work is concerned with the construction of preconditioners for indefinite linear systems. The systems under investigation arise in the numerical solution of quadratic programming problems, for example in the form of Karush–Kuhn–Tucker (KKT) optimality conditions or in interior–point methods. Therefore, the system matrix is referred to as a KKT matrix. It is not the p...

Multi-objective reliability-based design optimization (MORBDO) is an efficient tool for generating reliable Pareto-optimal (PO) solutions. However, such PO solutions requires many function evaluations reliability analysis, thereby increasing the computational cost. In this paper, a single-loop multi-objective formulation proposed that approximates analysis using Karush-Kuhn Tucker (KKT) optimal...

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved und...

In this paper, we consider an interior point method for nonlinear semidefinite programming. Yamashita, Yabe and Harada presented a primal-dual interior point method in which a nondifferentiable merit function was used. By using shifted barrier KKT conditions, we propose a differentiable primal-dual merit function within the framework of the line search strategy, and prove the global convergence...

This paper points out an important source of inefficiency in Smola and Schölkopf's sequential minimal optimization (SMO) algorithm for support vector machine (SVM) regression 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 for regression. These modified algorithm...

In this paper we consider a class of non-Lipschitz and non-convex minimization problems which generalize the L2 − Lp minimization problem. We propose an iterative algorithm that decides the next iteration based on the local convexity/concavity/sparsity of its current position. We show that our algorithm finds an -KKT point within O(log −1) iterations. The same result is also applied to the prob...