## A Predictor-Corrector Algorithm For A Class Of Nonlinear Saddle Point Problems (1994)

Venue: | SIAM Journal on Control and Optimization |

Citations: | 5 - 2 self |

### BibTeX

@ARTICLE{Sun94apredictor-corrector,

author = {Jie Sun and Jishan Zhu and Gongyun Zhao and Theta R},

title = {A Predictor-Corrector Algorithm For A Class Of Nonlinear Saddle Point Problems},

journal = {SIAM Journal on Control and Optimization},

year = {1994},

volume = {35},

pages = {532--551}

}

### OpenURL

### Abstract

. An interior path-following algorithm is proposed for solving the nonlinear saddle point problem minimax c T x + OE(x) + b T y \Gamma /(y) \Gamma y T Ax subject to (x; y) 2 X \Theta Y ae R n \Theta R m ; where OE(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 finds an ffl-optimal solution of the problem in O( p m+ nj log ¯=fflj) iterations if both OE(x) and /(y) satisfy a scaled Lipschitz condition. Keywords. Interior point methods, optimal control, saddle point problem, stochastic programming. Abbreviated title. IP method for saddle point problems AMS subject classifications. 49J35, 65K10, 90C06, 90C15, 90C33 October, 1994 This research is partially supported by grant...