TY - JOUR
T1 - A New Constraints Identification Technique-Based QP-Free Algorithm for the Solution of Inequality Constrained Minimization Problems
AU - Chang-yin Zhou, Guo-ping He & Yong-li Wang
JO - Journal of Computational Mathematics
VL - 5
SP - 591
EP - 608
PY - 2006
DA - 2006/10
SN - 24
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8777.html
KW - QP-free method, Optimization, Global convergence, Superlinear convergence, Constraints identification technique.
AB - <p style="text-align: justify;">In this paper, we propose a feasible QP-free method for solving nonlinear inequality constrained optimization problems. A new working set is proposed to estimate the active set. Specially, to determine the working set, the new method makes use of the multiplier information from the previous iteration, eliminating the need to compute a multiplier function. At each iteration, two or three reduced symmetric systems of linear equations with a common coefficient matrix involving only constraints in the working set are solved, and when the iterate is sufficiently close to a KKT point, only two of them are involved. Moreover, the new algorithm is proved to be globally convergent to a KKT point under mild conditions. Without assuming the strict complementarity, the convergence rate is superlinear under a condition weaker than the strong second-order sufficiency condition. Numerical experiments illustrate the efficiency of the algorithm.</p>