A Peaceman–Rachford Splitting Method with Monotone Plus Skew-Symmetric Splitting for Nonlinear Saddle Point Problems
作者： Weiyang Ding , Michael K. Ng , Wenxing Zhang
DOI: 10.1007/S10915-019-01034-W
关键词: Monotone polygon 、 Convex optimization 、 Linear system 、 Positive-definite matrix 、 Karush–Kuhn–Tucker conditions 、 Saddle point 、 Applied mathematics 、 Convexity 、 Hermitian matrix 、 Mathematics
摘要: This paper is devoted to solving the linearly constrained convex optimization problems by Peaceman–Rachford splitting method with monotone plus skew-symmetric on KKT operators. approach generalizes Hermitian and skew-Hermitian method, an unconditionally convergent algorithm for non-Hermitian positive definite linear systems, nonlinear scenario. The convergence of proposed guaranteed under some mild assumptions, e.g., strict convexity objective functions consistency constraints, even though Lions–Mercier property not fulfilled. In addition, we explore inexact version algorithm, which allows subproblems approximately inexactness criteria. Numerical simulations image restoration problem demonstrate compelling performance algorithm.
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