Adaptive approximation models in optimization (Q1905200)

In the paper a method for optimization of functions of several variables that substantially reduces the number of objective function evaluations compared with traditional methods is introduced. The method is based on the property of iterative refinement of approximation models of the optimized function in the approximation domains that contract to the extremum point. The proposed method does not require subjective specification of the starting point, steplength, or the parameters of the search procedure. The method is designed for efficient optimization of unimodal functions of several (in the practice not more than 10-15) variables and can be applied to find the global extremum of polymodal functions and also for optimization of scalarized forms of various vector objective functions.