Using the fact that any two player discounted stochastic game with finite state and action spaces can be recast as a non-convex constrained optimization problem, where each global minima corresponds to a stationary Nash equilibrium, we present a sequential quadratic programming based algorithm that converges to a KKT point. This KKT point is an -Nash equilibrium for some > 0 and under some suit...

Aims. We previously reported that kamikihito (KKT), a traditional Japanese medicine, improved memory impairment and reversed the degeneration of axons in the 5XFAD mouse model of Alzheimer's disease (AD). However, the mechanism underlying the effects of KKT remained unknown. The aim of the present study was to investigate the mechanism by which KKT reverses the progression of axonal degeneratio...

We consider optimality systems of Karush-Kuhn-Tucker (KKT) type, which arise, for example, as primal-dual conditions characterizing solutions of optimization problems or variational inequalities. In particular, we discuss error bounds and Newton-type methods for such systems. An exhaustive comparison of various regularity conditions which arise in this context is given. We obtain a new error bo...

Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Approximate KKT and Approximate Gradient Projection conditions are analyzed in this work. These conditions are not necessarily equivalent. Implications between different conditions and counter-examples will be shown. Algorithmic consequences will be discussed.

The hybrid cellular automaton (HCA) algorithm was inspired by the structural adaptation of bones to their ever changing mechanical environment. This methodology has been shown to be an effective topology synthesis tool. In previous work, it has been observed that the convergence of the HCA methodology is affected by parameters of the algorithm. As a result, questions have been raised regarding ...

This paper deals with optimality conditions to solve nonlinear programming problems. The classical Karush-Kuhn-Tucker (KKT) optimality conditions are demonstrated through a cone approach, using the well known Farkas’ Lemma. These conditions are valid at a minimizer of a nonlinear programming problem if a constraint qualification is satisfied. First we prove the KKT theorem supposing the equalit...

Abstract In this paper, weak optimal inverse problems of interval linear programming (IvLP) are studied based on KKT conditions. Firstly, the problem is precisely defined. Specifically, by adjusting minimum change current cost coefficient, a given solution can become optimal. Then, an equivalent characterization IvLP obtained. Finally, simplified without coefficient null variable.

The paper rst investigates Newton-type methods for generalized equations with compact solution sets. The analysis of their local convergence behavior is based, besides other conditions, on the upper Lipschitz-continuity of the local solution set mapping of a simply perturbed generalized equation. This approach is then applied to the KKT conditions of a nonlinear program with inequality constrai...

In this paper we consider the bilevel programming problem (BLPP), which is a sequence of two optimization problems where the constraint region of the upper-level problem is determined implicitly by the solution set to the lower-level problem. We extend well-known constraint qualifications for nonlinear programming problems such as the Abadie constraint qualification, the Kuhn-Tucker constraint ...

The global convergence of ADMM for convex problems was given by He and Yuan in [5] under the variation inequality framework. However, since our optimization problem is non-convex, the convergence analysis for ADMM needs additional conditions. In non-convex optimization, convergence to a stationary point (local minimum) is the best convergence property that we can hope for. By imposing some cond...