Theoretical and computational aspects of the optimal design centering, tolerancing, and tuning problem

The optimal design centering, tolerancing, and tuning problem is transcribed into a mathematical programming problem of the form , , , continuously differentiable, and compact subsets of , . A simplified form of , is discussed. It is shown that is locally Lipschitz continuous but not continuously differentiable. Optimality conditions for based on the concept of generalized gradients are derived. An algorithm, consisting of a master outer approximations algorithm proposed by Gonzaga and Polak and of a new subalgorlthm for nondifferentiable problems of the form , where is a discrete set, is presented. The subalgorlthm, an extension of Polak\´s method of feasible directions to nondifferentlable problems, is shown to converge under suitable assumptions. Moreover, the optimality function used in the subalgorithm is proven to satisfy a condition which guarantees that the overall algorithm converges.