Dual quasi-Newton algorithm for infinitely constrained optimization problems

This paper deals with an infinitely constrained optimization problem-a nonlinear programming problem with an infinite number of constraints. This problem can be regarded as a satisfaction optimization problem, in which an objective function is to be minimized subject to the satisfaction condtions that plural performance criteria should be kept below the prescribed permissible level even under the worst situation. As computational methods for the problems of this sort, there are the relaxation algorithm and the nondifferentiable optimization algorithm. In this paper, the authors propose the dual quasi-Newton algorithm as a direct method for infinitely constrained optimization problems. First of all, this class of problems is reformulated as an optimization problem with an infinite-dimensional inequality constraint by introducing an abstract operator; then the quasi-Newton method is applied to the abstract optimization problem. This means that an infinite number of constraints are simultaneously taken into account. The subsidiary problems for direction-finding are still infinitely constrained, but their dual problems are nonnegatively constrained quadratic programming problems in a function space and they can be easily solved by clipping-off techniques without any relaxation or applying nondifferentiable optimization algorithms. [In Japanese.]