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In the paper, the global optimization problem of a multidimensional " black-box " function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. A new efficient algorithm for solving this problem is presented. At each iteration of the method a number of possible Lipschitz constants is chosen from a set of… (More)

In many practical decision-making problems it happens that functions involved in optimization process are black-box with unknown analytical representations and hard to evaluate. In this paper, a global optimization problem is considered where both the goal function f (x) and its gradient f ′ (x) are black-box functions. It is supposed that f ′ (x) satisfies… (More)

In many important design problems, some decisions should be made by finding the global optimum of a multiextremal objective function subject to a set of constrains. Frequently, especially in engineering applications , the functions involved in optimization process are black-box with unknown analytical representations and hard to evaluate. Such… (More)

A procedure for generating non-differentiable, continuously differentiable, and twice continuously differentiable classes of test functions for multiextremal multidimensional box-constrained global optimization is presented. Each test class consists of 100 functions. Test functions are generated by defining a convex quadratic function systematically… (More)

In the paper, a global optimization problem is considered where the objective function f (x) is univariate, black-box, and its first derivative f ′ (x) satisfies the Lipschitz condition with an unknown Lipschitz constant K. In the literature, there exist methods solving this problem by using an a priori given estimate of K, its adaptive estimates, and… (More)

In this paper, global optimization (GO) Lipschitz problems are considered where the multi-dimensional multiextremal objective function is determined over a hyperinterval. An efficient one-dimensional GO method using local tuning on the behavior of the objective function is generalized to the multi-dimensional case by the diagonal approach using two… (More)

A global optimization problem is studied where the objective function f (x) is a multidimensional black-box function and its gradient f ′ (x) satisfies the Lip-schitz condition over a hyperinterval with an unknown Lipschitz constant K. Different methods for solving this problem by using an a priori given estimate of K, its adaptive estimates, and adaptive… (More)

Lipschitz one-dimensional constrained global optimization (GO) problems where both the objective function and constraints can be multiextremal and non-differentiable are considered in this paper. Problems, where the constraints are verified in an a priori given order fixed by the nature of the problem are studied. Moreover, if a constraint is not satisfied… (More)