Continuous global optimization of multivariable functions based on Sergeev and Kvasov diagonal approach

Abstract. One of modern global optimization algorithms is method Strongin and Piyavskii modified by Sergeev Kvasov diagonal approach. In recent paper we propose an extension this approach to continuous multivariable functions defined on the multidimensional parallelepiped. It known that applies only a Lipschitz function though it effectively extends one-dimensional algorithm case. So authors modify We mentioned using introduced Vanderbei ε-Lipschitz property generalizes conventional inequality. proved real valued uniformly convex domain if ε-Lipschitz. Because parallelepiped compact set, demand objective be search domain. describe extended Strongin’s Piyavskii’s methods in modification prove sufficient conditions for convergence. As example proposed method’s application, at end article show numerical results different but not three partition strategies: “partition 2”, 2N” “effective”. For first two them present formulas computing new iteration point recalculating constant estimate. also allows find any algorithm’s step.