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Now showing items 11-20 of 21
Condition-Measure Bounds on the Behavior of the Central Trajectory of a Semi-Definete Program
(Massachusetts Institute of Technology, Operations Research Center, 1999-08)
We present bounds on various quantities of interest regarding the central trajectory of a semi-definite program (SDP), where the bounds are functions of Renegar's condition number C(d) and other naturally-occurring quantities ...
Pre-Conditioners and Relations between Different Measures of Conditioning for Conic Linear Systems
(Massachusetts Institute of Technology, Operations Research Center, 2000-06)
In recent years, new and powerful research into "condition numbers" for convex optimization has been developed, aimed at capturing the intuitive notion of problem behavior. This research has been shown to be important in ...
A Potential Reduction Algorithm With User-Specified Phase I - Phase II Balance, for Solving a Linear Program from an Infeasible Warm Start
(Massachusetts Institute of Technology, Operations Research Center, 1991-10)
This paper develops a potential reduction algorithm for solving a linear-programming problem directly from a "warm start" initial point that is neither feasible nor optimal. The algorithm is of an "interior point" variety ...
Fabrication-Adaptive Optimization, with an Application to Photonic Crystal Design
(Massachusetts Institute of Technology, Operations Research Center, 2013-07-22)
Some Characterizations and Properties of the "Distance to Ill-Posedness" and the Condition Measure of a Conic Linear System
(Massachusetts Institute of Technology, Operations Research Center, 1995-10)
A conic linear system is a system of the form P: find x that solves b- Ax E Cy, E Cx, where Cx and Cy are closed convex cones, and the data for the system is d = (A, b). This system is"well-posed" to the extent that (small) ...
Prior Reduced Fill-In in Solving Equations in Interior Point Algorithms
(Massachusetts Institute of Technology, Operations Research Center, 1990-07)
The efficiency of interior-point algorithms for linear programming is related to the effort required to factorize the matrix used to solve for the search direction at each iteration. When the linear program is in symmetric ...
On Two Measures of Problem Instance Complexity and Their Correlation with the Performance of SeDuMi on Second-Order Cone Problems
(Massachusetts Institute of Technology, Operations Research Center, 2004-09-13)
We evaluate the practical relevance of two measures of conic convex
problem complexity as applied to second-order cone problems solved using
the homogeneous self-dual (HSD) embedding model in the software
SeDuMi. The ...
Computation of Minimum Volume Covering Ellipsoids
(Massachusetts Institute of Technology, Operations Research Center, 2002-07)
We present a practical algorithm for computing the minimum volume n-dimensional ellipsoid that must contain m given points al,...,am C Rn . This convex constrained problem arises in a variety of applied computational ...
Projective Transformations for Interior Point Methods, Part II: Analysis of An Algorithm for Finding the Weighted Center of a Polyhedral System
(Massachusetts Institute of Technology, Operations Research Center, 1988-06)
In Part II of this study, the basic theory of Part I is applied to the problem of finding the w-center of a polyhedral system X . We present a projective transformation algorithm, analagous but more general than Karmarkar's ...