3-1 Piecewise NCP Function for New Nonmonotone QP-Free Infeasible Method
Ailan Liu*,** and Dingguo Pu*,***
*Department of Mathematics, Tongji University, No.1239, Siping Road, Shanghai 200092, China
**School of Mathematics and Physics, Shanghai University of Electric Power, No.2588, Changyang Road, Yangpu District, Shanghai, China
***School of Mathematics and Statistics, Henan University of Science and Technology, No.263, Kaiyuan Road, Luoyang 471023, China
We propose a nonmonotone QP-free infeasible method for inequality-constrained nonlinear optimization problems based on a 3-1 piecewise linear NCP function. This nonmonotone QP-free infeasible method is iterative and is based on nonsmooth reformulation of KKT first-order optimality conditions. It does not use a penalty function or a filter in nonmonotone line searches. This algorithm solves only two systems of linear equations with the same nonsingular coefficient matrix, and is implementable and globally convergent without a linear independence constraint qualification or a strict complementarity condition. Preliminary numerical results are presented.
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