An Infeasible Active Set Method with Combinatorial Line Search for Convex Quadratic Problems with Bound Constraints

The minimization of a convex quadratic function under bound constraints is a fundamental building block for more complicated optimization problems. The active-set method introduced by [M. Bergounioux, K. Ito, and K. Kunisch. Primal-Dual Strategy for Constrained Optimal Control Problems. SIAM Journal on Control and Optimization, 37:1176–1194, 1999.] and [M. Bergounioux, M. Haddou, M. Hintermüller, and … Read more

A recursive semi-smooth Newton method for linear complementarity problems

A primal feasible active set method is presented for finding the unique solution of a Linear Complementarity Problem (LCP) with a P-matrix, which extends the globally convergent active set method for strictly convex quadratic problems with simple bounds proposed by [P. Hungerlaender and F. Rendl. A feasible active set method for strictly convex problems with … Read more

A feasible active set method for strictly convex problems with simple bounds

A primal-dual active set method for quadratic problems with bound constraints is presented which extends the infeasible active set approach of [K. Kunisch and F. Rendl. An infeasible active set method for convex problems with simple bounds. SIAM Journal on Optimization, 14(1):35-52, 2003]. Based on a guess of the active set, a primal-dual pair (x,α) … Read more