We consider the applicability of stochastic global optimization algorithms on test-functions whose domain of definition is a simply-connected and finite interval of real numbers. We argue on the basis of theoretical reflections of statistical physics (namely random-walk) and computer simulations...

Global optimization (GO) is one of the key numerical tools in computational physics. Among the GO algorithms the ones originating in statistical physics are particularly powerful. Recently an adaptive scheme was developed to increase the efficiency of one of these algorithms (stochastic...

In this paper, we introduce a generalized proximal Lagrangian function for the constrained nonlinear programming problem and discuss existence of its saddle points. In particular, the local saddle point is obtained by using the second-order sufficient conditions, and the global saddle point is...

Fitness landscape theory is a mathematical framework for numerical analysis of search algorithms on combinatorial optimization problems. We study a representation of fitness landscape as a weighted directed graph. We consider out forest and in forest structures in this graph and establish...