ON STABLE CONSTRUCTION OF MINIMIZING SEQUENCES IN NONLINEAR PROGRAMMING PROBLEMS WITH EQUALITY AND INEQUALITY CONSTRAINTS |
| 3 | |
| 2013 |
| scientific article | 519.85 | ||
| 212-222 | nonlinear programming, parametric problem, sequential optimization, proximal subgradient, Lagrange principle, Kuhn-Tucker vector, minimizing approximate solution, duality, regularization. |
| The article describes the dual regularization approach applied to the general parametric nonlinear programming problem in a Hilbert space with an infinite-dimensional equality constraint and a finite number of functional inequality constraints. This method provides a stable (in relation to the input data errors) construction of minimizing sequence elements in the original problem from elements of sequences that minimize the modified Lagrange function taken at the values of the dual variables of the respective maximizing sequence in the modified dual problem. In particular, it is shown how generalized differentiability properties of the lower semicontinuous value functions in infinite-dimensional problems of mathematical programming generate corresponding constructions of the modified Lagrange functions. An example is given to illustrate the instability of the formal construction of minimizing sequences without the solution regularization of the modified dual problem. |
 |