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A Global and Quadratically-Convergent Method for Linear $L_{\infty}$ Problems

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Abstract

We propose a new global and quadratically convergent algorithm for the linear l problem. This method works on the piecewise l problem directly by generating descent directions - via a sequence of weighted least squares problems - and using piecewise linear linesearches to ensure a decrease in the l function at every step. We prove that ultimately full Newton-like steps are taken where the Newton step is based on the complementary slackness condition holding at the solution. Numerical results suggest a very promising method; the number of iterations required to achieve high accuracy is relatively insensitive to problem size.

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1990-04

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Cornell University

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computer science; technical report

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http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR90-1121

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technical report

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