Approximate method of optimization of nonlinear programming problems

Currently, the problem of choosing optimal solution is one most important and urgent problems in industry, economy, agriculture military sphere. Methods approaches theory nonlinear programming are used to solve many applied optimization problems. The main difficulty lack a universal method for solving this class To problem, special methods being developed particular problems, example, positive or limited initial data. paper investigates analytical purpose work develop new approximate function under constraints form equalities. do this, an approximation (expansion series) objective performed. All variables considered bounded at top bottom. infinitely differentiable by set arguments, all their derivatives assumed be absolute value given number. In article, theorem on conditional maximum proved. results which justification method. Since approximate, error proposed representation constraint functions estimated. nature, boundaries variable changes often approximately they can adjusted. addition, it possible adjust point relative decomposed into series. Therefore, article analyzes sensitivity when changing decomposition series different values coordinates left searching function. explain operation method, specific numerical example analyzed detail. Modeling MS Excel environment was it. Graphs study data constructed. Nonlinear models used, following practically issues: minimizing costs sale products, optimizing consumer choice, maximizing production volume, determining rational behavior individual situation, use resources, forming portfolio securities.