We consider mass-constrained minimizers for a class of non-convex energy functionals involving double-well potentials. Based upon global convex lower bounds to the energy, we introduce a simple strategy to find sufficient conditions on a given critical point (metastable state) to be a global minimizer. We show that this strategy works well for the one exact and known metastable state: the const...

For a class of 2-D elastic energies we show that a radial equilibrium solution is the unique global minimizer in a subclass of all admissible maps. The boundary constraint is a double cover of S; the minimizer u is C and is such that det∇u vanishes at one point. Mathematics Subject Classification. — Please, give AMS classification codes —. Received October 28, 2005. Revised March 31, 2006.

Global optimization is necessary in some cases when we want to achieve the best solution or we require a new solution which is better the old one. However global optimization is a hazard problem. Gradient descent method is a well-known technique to find out local optimizer whereas approximation solution approach aims to simplify how to solve the global optimization problem. In order to find out...

Inspired by a method by Jones et al. (1993), we present a global optimization algorithm based on multilevel coordinate search. It is guaranteed to converge if the function is continuous in the neighborhood of a global minimizer. By starting a local search from certain good points, an improved convergence result is obtained. We discuss implementation details and give some numerical results.

In this paper bearing the same title as our earlier survey-paper [11] we pursue the goal of characterizing the global solutions of an optimization problem, i.e. getting at necessary and sufficient conditions for a feasible point to be a global minimizer (or maximizer) of the objective function. We emphasize nonconvex optimization problems presenting some specific structures like ‘convexanticonv...

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the εk-global minimization of the Augmented Lagrangian with simple constraints, where εk → ε. Global convergence to an ε-global minimizer of the original problem is proved. The subproblems are solved...

In many global optimization problems motivated by engineering applications, the number of function evaluations is severely limited by time or cost. To ensure that each of these evaluations contributes to the localization of good candidates for the role of global minimizer, a sequential choice of evaluation points is usually carried out. In particular, when Kriging is used to interpolate past ev...