A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems - Kojima, Masakazu
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Présentation A Unified Approach To Interior Point Algorithms For Linear Complementarity Problems Format Broché
- Livre Littérature Générale
Résumé :
Following Karmarkar's 1984 linear programming algorithm, numerous interior-point algorithms have been proposed for various mathematical programming problems such as linear programming, convex quadratic programming and convex programming in general. This monograph presents a study of interior-point algorithms for the linear complementarity problem (LCP) which is known as a mathematical model for primal-dual pairs of linear programs and convex quadratic programs. A large family of potential reduction algorithms is presented in a unified way for the class of LCPs where the underlying matrix has nonnegative principal minors (P0-matrix). This class includes various important subclasses such as positive semi-definite matrices, P-matrices, P*-matrices introduced in this monograph, and column sufficient matrices. The family contains not only the usual potential reduction algorithms but also path following algorithms and a damped Newton method for the LCP. The main topics are global convergence, global linear convergence, and the polynomial-time convergence of potential reduction algorithms included in the family.
Sommaire:
This monograph presents a study of interior-point algorithms for the linear complementarity problem, known as a mathematical model for primal-dual pairs of linear programs and convex quadratic programs. A large class of potential reduction algorithms is presented in a unified way....
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