Interior-Point Methods for Convex Programming

Abstract

This work is concerned with generalized convex programming problems, where the objective and also the constraints belong to a certain class of convex functions. It examines the relationship of two conditions for generalized convex programming--self concordance and a relative Lipschitz condition--and gives an outline for a short and simple analysis of an interior-point method for generalized convex programming. It generalizes ellipsoidal approximations for the feasible set, and in the special case of a nondegenerate linear program it establishes a uniform bound on the condition number of the matrices occurring when the iterates remain near the path of centers.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1990
Accession Number
ADA231372

Entities

People

  • Florian Jarre

Organizations

  • Stanford University

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algebraic Functions
  • Algorithms
  • Boundaries
  • Convergence
  • Convex Programming
  • Convex Sets
  • Geometry
  • Guarantees
  • Inequalities
  • Linear Programming
  • Numbers
  • Operations Research
  • Polynomials
  • Sequences
  • Topology
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.