An O((k + 1){sup 2}nL) infeasible-interior-point
The P*-matrix linear complementarity problem requires the computation of a vector pair (x, s) {element_of} R{sup n{times}n} is a P*-matrix. The class of P*-matrices was introduced by Kojima, Megiddo, Noma and Yoshise and it contains many types of matrices (positive) semi-definite matrices and P-matrices, etc. Most interior-point methods for linear programming have been successfully extended to the monotone LCP, a special case of P*-matrix LCP. A potential reduction method for P{sub *}-matrix LCP was proposed by Kojima et al. Their method solves the LCP in at most O((1 + k) {radical}nL) iterations. However, no superliner convergence results have been proved so far for that method. The algorithm given by Miao enjoys both polynomial complexity and quadratic convergence. All these methods mentioned above require a strictly feasible starting point. In practice, it is difficult to get such an initial point. In this talk, we will propose a modified predictor-corrector infeasible-interior-point algorithm for solving the P*-matrix LCP. Two matrix factorizations and two backsolves are to be computed at each iteration. The algorithm terminates in O((k + 1){sup 2}nl) steps either by finding a solution or by determining that the problem has no solutions of norm less than a given constant. Our algorithm also enjoys the quadratic convergence.
- OSTI ID:
- 36168
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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