On Polaroid Intersections

Abstract

Polaroid sets and functions have been introduced as a new tool, with applications in non-linear programming, particularly in quasi-concave and integer optimization problems over a linearly constrained set of feasible solutions. The name polar programming applies to a general class of non-linear mathematical programming problems which can be solved by the polaroid approach. In integer programming polaroids yield non-trivial extensions of the intersection cut approach. The paper builds on the properties of polaroid sets (particularly complete convex polaroids) and focuses on the following intersection problem: Given a point x bar belonging to the polaroid set P*, find the intersection point u* of a one-dimensional ray u with the boundary of P*.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1972
Accession Number
AD0743265

Entities

People

  • Claude-alain Burdet

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Computations
  • Computer Programming
  • Computing-Related Activities
  • Construction
  • Evolutionary Algorithms
  • Integer Programming
  • Linear Programming
  • Mathematical Programming
  • Military Research
  • Optimization
  • Schools
  • Supply Chain Management
  • Universities

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Operations Research