Using necessary optimality conditions for acceleration of the nonuniform covering optimization method

Paper deals with the non-uniform covering method that is aimed at deterministic global optimization. This method finds a feasible solution to the optimization problem numerically and proves that the obtained solution differs from the optimal by no more than a given accuracy. Numerical proof consists of constructing a set of covering sets - the coverage. The number of elements in the coverage can be very large and even exceed the total amount of available computer resources. Basic method of coverage construction is the comparison of upper and lower bounds on the value of the objective function. In this work we propose to use necessary optimality conditions of first and second order for reducing the search for boxconstrained problems. We provide the algorithm description and prove its correctness. The efficiency of the proposed approach is studied on test problems.