114 research outputs found
An Interior-Point Method with Polynomial Complexity and Superlinear Convergence for Linear Complementarity Problems
For linear programming, a primal-dual interior-point algorithm was recently constructed by Zhang and Tapia that achieves both polynomial complexity and Q-superlinear convergence (Q-quadratic in the nondegenerate case). In this paper, we extend their results to quadratic programming and linear complementarity problems
Introducing Interior-Point Methods for Introductory Operations Research Courses and/or Linear Programming Courses
In recent years the introduction and development of Interior-Point Methods has had a profound impact on optimization theory as well as practice, influencing the field of Operations Research and related areas. Development of these methods has quickly led to the design of new and efficient optimization codes particularly for Linear Programming. Consequently, there has been an increasing need to introduce theory and methods of this new area in optimization into the appropriate undergraduate and first year graduate courses such as introductory Operations Research and/or Linear Programming courses, Industrial Engineering courses and Math Modeling courses. The objective of this paper is to discuss the ways of simplifying the introduction of Interior-Point Methods for students who have various backgrounds or who are not necessarily mathematics majors
Convergence Analysis of an Inexact Feasible Interior Point Method for Convex Quadratic Programming
In this paper we will discuss two variants of an inexact feasible interior
point algorithm for convex quadratic programming. We will consider two
different neighbourhoods: a (small) one induced by the use of the Euclidean
norm which yields a short-step algorithm and a symmetric one induced by the use
of the infinity norm which yields a (practical) long-step algorithm. Both
algorithms allow for the Newton equation system to be solved inexactly. For
both algorithms we will provide conditions for the level of error acceptable in
the Newton equation and establish the worst-case complexity results
Interior point methods : current status and future directions
Cover title.Includes bibliographical references (leaves 23-24).Robert Freund and Shinji Mizuno
Interior point methods : current status and future directions
Cover title.Includes bibliographical references (leaves 23-24).Robert Freund and Shinji Mizuno
Optimization and Applications
Proceedings of a workshop devoted to optimization problems, their theory and resolution, and above all applications of them. The topics covered existence and stability of solutions; design, analysis, development and implementation of algorithms; applications in mechanics, telecommunications, medicine, operations research
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