A Moving Balls Approximation Method for a Class of Smooth Constrained Minimization Problems

Abstracts of invited talks blancos of invited talks blanco A moving balls approximation method for a class of smooth constrained minimization Alfred Auslender Université de Lyon, France We introduce a new algorithm for a class of smooth constrained minimization problems which is an iterative scheme that generates a sequence of feasible points that approximates the constraints set by a sequence of balls, and is accordingly called the Moving Balls Approximation Algorithm (MBA). The computational simplicity of MBA, which uses first order data information makes it suitable for large scale problems. Theoretical and computational properties of MBA and of some variant, in its primal and dual forms are studied, and convergence and global rate of convergence results are established for nonconvex and convex problems. Extension of MBA is also developed for a class of variational inequalities. Initial numerical experiments on quadratically constrained problems demonstrate the viability and performance when compared to some existing state-of-the-art optimization methods/software such as an SQP solver from the IMSL Library, and the CVXOPT software package for convex optimzation. Based on a common work with Ron Shefi and Marc Teboulle, School of Mathematical Sciences Tel-Aviv University, Israel.