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A QP-free algorithm of quasi-strongly sub-feasible directions for inequality constrained optimization

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  • In this paper, combining the method of quasi-strongly sub-feasible directions (MQSSFD) and the working set technique, a new QP-free algorithm with an arbitrary initial iteration point for solving inequality constrained optimization is proposed. At each iteration, the algorithm solves only two systems of linear equations with a same uniformly nonsingular coefficient matrix to obtain the search direction. Furthermore, the positive definiteness assumption on the Hessian estimate is relaxed. Under some necessary assumptions, the new algorithm not only possesses global and strong convergence, but also ensures that the iteration points can get into the feasible set after finite iterations. Finally, a series of preliminary numerical results are reported to show that the algorithm is promising.
    Mathematics Subject Classification: Primary: 90C30, 49M37; Secondary: 65K05.


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