Parametric optimization with applications to optimal control and sequential quadratic programming. (English) Zbl 0734.90094

Alt, Walter

Bayreuther Math. Schr. 35, 1-37 (1991).

The author investigates existence, uniqueness and continuity of solutions to nonlinear parametric optimization problems in Banach spaces. He assumes that constraint regularity, a strong second-order sufficient optimality condition, and a stability condition for the Lagrange multipliers, replacing the condition of linear independence of the gradients of active constraints in finite dimensions, hold at a local minimizer of the reference problem. Under these conditions he proves that for sufficiently smooth perturbations of the constraints and the objective function, both the optimal solutions and the associated multipliers are locally single-valued and continuous functions of the parameter. The results are established using an implicit function theorem for strongly regular generalized equations of S. M. Robinson. The results are applied to investigate stability of optimal control problems and local convergence properties of a sequential quadratic programming method for infinite-dimensional optimization problems.

Reviewer: M. Z. Nashed (Newark/Delaware)

MSC:

90C31	Sensitivity, stability, parametric optimization
90C48	Programming in abstract spaces
49K40	Sensitivity, stability, well-posedness
90C30	Nonlinear programming

Keywords:

existence, uniqueness and continuity of solutions; nonlinear parametric optimization; Banach spaces; constraint regularity; strong second-order sufficient optimality condition; stability of optimal control; sequential quadratic programming; infinite-dimensional optimization