A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Weak sharp minima in mathematical programming
SIAM Journal on Control and Optimization
NE/SQP: a robust algorithm for the nonlinear complementarity problem
Mathematical Programming: Series A and B
Nonlinear complementarity as unconstrained and constrained minimization
Mathematical Programming: Series A and B - Special issue: Festschrift in Honor of Philip Wolfe part II: studies in nonlinear programming
On the resolution of monotone complementarity problems
Computational Optimization and Applications
Some methods based on the D-gap function for solving monotone variational inequalities
Computational Optimization and Applications - Special issue on nonsmooth and smoothing methods
A primal-dual algorithm for minimizing a sum of Euclidean norms
Journal of Computational and Applied Mathematics
Local convergence analysis of projection-type algorithms: unified approach
Journal of Optimization Theory and Applications
SIAM Journal on Optimization
Semismooth Newton Methods for Solving Semi-Infinite Programming Problems
Journal of Global Optimization
An iterative method for solving semismooth equations
Journal of Computational and Applied Mathematics - Special issue: Papers presented at the 1st Sino--Japan optimization meeting, 26-28 October 2000, Hong Kong, China
An interior-point affine-scaling trust-region method for semismooth equations with box constraints
Computational Optimization and Applications
Journal of Computational and Applied Mathematics
A nonsmooth Levenberg-Marquardt method for solving semi-infinite programming problems
Journal of Computational and Applied Mathematics
The Semismooth Approach for Semi-Infinite Programming without Strict Complementarity
SIAM Journal on Optimization
Convergence properties of nonmonotone spectral projected gradient methods
Journal of Computational and Applied Mathematics
A new smoothing Newton-type algorithm for semi-infinite programming
Journal of Global Optimization
Hi-index | 0.00 |
In this paper, in order to solve semismooth equations with box constraints, we present a class of smoothing SQP algorithms using the regularized-smooth techniques. The main difference of our algorithm from some related literature is that the correspondent objective function arising from the equation system is not required to be continuously differentiable. Under the appropriate conditions, we prove the global convergence theorem, in other words, any accumulation point of the iteration point sequence generated by the proposed algorithm is a KKT point of the corresponding optimization problem with box constraints. Particularly, if an accumulation point of the iteration sequence is a vertex of box constraints and additionally, its corresponding KKT multipliers satisfy strictly complementary conditions, the gradient projection of the iteration sequence finitely terminates at this vertex. Furthermore, under local error bound conditions which are weaker than BD-regular conditions, we show that the proposed algorithm converges superlinearly. Finally, the promising numerical results demonstrate that the proposed smoothing SQP algorithm is an effective method.