Algorithms for Nonlinear Programming.

Abstract

Several algorithms for solving problems in linear, quadratic, and nonlinear programming, network flows, and facilities location were developed and analyzed. Results include: (1) The analysis of the computational complexity of the problem of determining an optimally sparse representation of the null space of a matrix, and the development of worst-case bounds for the shadow-vertex simplex algorithm and several heuristics for distance constrained discrete facility location problems and conditional covering problems; (2) The development of efficient algorithms for dense and sparse assignment problems, strictly convex quadratic programming problems, and a nonlinear programming problem that arises when maximizing a correlation coefficient subject to linear constraints; and (3) The application of iterative methods to large sparse equality-constraind quadratic programs and the development of multiple constraint deletion strategies for active-set algorithms for linearly consrained nonlinear programming problems. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 30, 1985
Accession Number
ADA161746

Entities

People

  • Donald Goldfarb

Organizations

  • Columbia University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Computational Complexity
  • Evolutionary Algorithms
  • Linear Programming
  • Mathematical Programming
  • Mathematics
  • Military Research
  • New York
  • Nonlinear Programming
  • Numerical Analysis
  • Operations Research
  • Optimization
  • Quadratic Programming
  • Simplex Method
  • Systems Engineering

Fields of Study

  • Computer science

Readers

  • Operations Research

Technology Areas

  • Space