Abstract Global optimization problems where evaluation of the objective function is an expensive operation arise frequently in engineering, decision making, optimal control, etc. There exist two huge but almost completely disjoint communities (they have different journals, conferences, test functions, etc.) solving these problems: a broad community practitioners using stochastic nature-inspired metaheuristics and people from academia studying deterministic mathematical programming methods....

A procedure for generating non-differentiable, continuously differentiable, and twice differentiable classes of test functions multiextremal multidimensional box-constrained global optimization is presented. Each class consists 100 functions. Test are generated by defining a convex quadratic function systematically distorted polynomials in order to introduce local minima. To determine class, the user defines following parameters: (i) problem dimension, (ii) number minima, (iii) value...

In the paper, global optimization problem of a multidimensional "black-box" function satisfying Lipschitz condition over hyperinterval with an unknown constant is considered. A new efficient algorithm for solving this presented. At each iteration method number possible constants are chosen from set values varying zero to infinity. This idea unified diagonal partition strategy. novel technique balancing usage local and information during partitioning proposed. procedure finding lower bounds...

In this survey, a recent computational methodology paying special attention to the separation of mathematical objects from numeral systems involved in their representation is described. It has been introduced with intention allow one work infinities and infinitesimals numerically unique framework all situations requiring these notions. The does not contradict Cantor's non-standard analysis views based on Euclid's Common Notion no. 5 "The whole greater than part" applied quantities (finite,...

A new computational methodology for executing calculations with infinite and infinitesimal quantities is described in this paper.It based on the principle 'The part less than whole' introduced by Ancient Greeks applied to all numbers (finite, infinite, infinitesimal) sets processes (finite infinite).It shown that it becomes possible write down finite, a finite number of symbols as particular cases unique framework.The has allowed us introduce Infinity Computer working such (its simulator...

We propose an algorithm using only the values of objective function for solving unconstrained global optimization problems. This belongs to class information methods introduced by Strongin [Numerical Methods in Multiextremal Problems, Nauka, Moskow,1978] and differs from other algorithms this presence local tuning which spies on changes Lipschitz constant over different sectors search region. describe two versions method: one-dimensional problems multidimensional (using Peano-type...

This paper deals with two kinds of the one-dimensional global optimization problems over a closed finite interval: (i) objective function $f(x)$ satisfies Lipschitz condition constant $L$; (ii) first derivative $M$. In paper, six algorithms are presented for case and (ii). both cases, auxiliary functions constructed adaptively improved during search. (i), piece-wise linear in smooth quadratic used. The constants $L$ $M$ either taken as values known priori or dynamically estimated A recent...