An Augmented Lagrangian Method for Optimization Problems in Banach Spaces

Augmented Lagrangian method for solving absolute value equation and its application in two-point boundary value problems

One of the most important topic that consider in recent years by researcher is absolute value equation (AVE). The absolute value equation seems to be a useful tool in optimization since it subsumes the linear complementarity problem and thus also linear programming and convex quadratic programming. This paper introduce a new method for solving absolute value equation. To do this, we transform a...

On an Augmented Lagrangian SQP Method for a Class of Optimal Control Problems in Banach Spaces

Mangasarian-Fromovitz and Zangwill Conditions For Non-Smooth Infinite Optimization problems in Banach Spaces

In this paper we study optimization problems with infinite many inequality constraints on a Banach space where the objective function and the binding constraints are Lipschitz near the optimal solution. Necessary optimality conditions and constraint qualifications in terms of Michel-Penot subdifferential are given.

A Hybrid Proximal Point Algorithm for Resolvent operator in Banach Spaces

Equilibrium problems have many uses in optimization theory and convex analysis and which is why different methods are presented for solving equilibrium problems in different spaces, such as Hilbert spaces and Banach spaces. The purpose of this paper is to provide a method for obtaining a solution to the equilibrium problem in Banach spaces. In fact, we consider a hybrid proximal point algorithm...

Lagrangian conditions for vector optimization in Banach spaces

We consider vector optimization problems on Banach spaces without convexity assumptions. Under the assumption that the objective function is locally Lipschitz we derive Lagrangian necessary conditions on the basis of Mordukhovich subdifferential and the approximate subdifferential by Ioffe using a non-convex scalarization scheme. Finally, we apply the results for deriving necessary conditions f...