علیرضا عطایی

In this thesis, we introduce an interior point constraint generation algorithm for semiinfinite optimization. We convert the semi-infinite problem to a linear problem using discretization and convert the linear problem to nonlinear problem using barrier function. In each iteration, we find a point near the central path, and we identify the finite number of deep constraints on the point is found in the infinite set of semi-infinite problems, and update the feasible region and barrier parameter. Then the feasibility for the new feasible region is recovered and the central path is updated. This process continues until the barrier parameter becomes safficiently small. We show that our algorithm stops with an "-solution to the SILO problem after adding at most O (m–22pˆ2 e3pm/") constraints, where – is the radius of the largest full dimensional ball contained in feasible region, pˆ is the maximum number of constraints added simultaneously and m is dimension of the semi infinite problem. we show that only O(p log (p ¯1)) Newton steps are required to obtain a point in the vicinity of the new feasible region. It is shown that interior point constraint generation algorithm is better than the classical interior point algorithm on problems with large number of constraints and small dimension.