A Predictor-corrector Algorithm for a Class of Nonlinear Saddle Point Problems
نویسندگان
چکیده
An interior path-following algorithm is proposed for solving the nonlinear saddle point problem minimax c T x + (x) + b T y ? (y) ? y T Ax subject to (x; y) 2 X Y R n R m ; where (x) and (y) are smooth convex functions and X and Y are boxes (hyper-rectangles). This problem is closely related to models in stochastic programming and optimal control studied by Rockafellar and Wets. Existence conditions on a central path are established. Starting from an initial solution near the central path with duality gap O(), the algorithm nds an-optimal solution of the problem in O(p m + nj log ==j) iterations if both (x) and (y) satisfy a scaled Lipschitz condition. Abbreviated title. IP method for saddle point problems
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