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.
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This section summarizes the main results of this paper . Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
parameters acen, potential reduction algorithm, column sufficient matrix, column sufficient matrices, interior feasible solutions, theoretical computational complexity, linear complementarity problems, interior point algorithms, final iterate, step size parameter, convex quadratic programs, convex quadratic programming, narrow neighborhood, smooth version, reduction algorithms New!
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This section summarizes the main results of this paper . Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
parameters acen, potential reduction algorithm, column sufficient matrix, column sufficient matrices, interior feasible solutions, theoretical computational complexity, linear complementarity problems, interior point algorithms, final iterate, step size parameter, convex quadratic programs, convex quadratic programming, narrow neighborhood, smooth version, reduction algorithms New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
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- A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems (Lecture Notes in Computer Science) by M. Kojima in Front Matter, and Back Matter
- Mathematical Programming: Essays in Honor of George B. Dantzig, Part II (Mathematical Programming Study) (Pt. 2) by Richard W. Cottle in Back Matter (1), and Back Matter (2)
- Efficient Query Processing in Geographic Information Systems (Lecture Notes in Computer Science) by Beng Chin Ooi in Back Matter
- System Modelling and Optimization (International Federation for Information Processing) by M. Iri in Back Matter
- Software Engineering Environments (Ellis Horwood Books in Information Technology) by Fred W. Long in Back Matter
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- Variational Analysis and Applications (Nonconvex Optimization and Its Applications (closed)) by Franco Giannessi on page 245, and page 256
- Object-Based Concurrent Computing: ECOOP '91 Workshop, Geneva, Switzerland, July 15-16, 1991. Proceedings (Lecture Notes in Computer Science) by Mario Tokoro in Back Matter
- Advances in Database Technology - EDBT '92: 3rd International Conference on Extending Database Technology, Vienna, Austria, March 23-27, 1992. Proceedings (Lecture Notes in Computer Science) by Alain Pirotte in Back Matter
- Constructivity in Computer Science: Summer Symposium, San Antonio, TX, June 19-22, 1991. Proceedings (Lecture Notes in Computer Science) by J.Paul Jr. Myers in Back Matter
- Computer Aided Systems Theory - EUROCAST '91: A Selection of Papers from the Second International Workshop on Computer Aided Systems Theory, Krems, ... (Lecture Notes in Computer Science) by Franz Pichler in Back Matter
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