A Subgradient Algorithm for Certain Minimax and Minisum Problems.

Abstract

This paper presents a subgradient algorithm for the problem Min <F(x); x an element of R to the n power> where F(x) = Max <f sub i(x); i = 1, 2, ..., m> and where f sub i(x) = sum over j of f sub ij(x). Each f sub ij is assumed to be a proper convex function, and the number of different subgradient sets associated with nondifferentiable points of f sub ij is assumed to be finite on any bounded set. Problems belonging to this class include those where the f sub ij are l sub p - norms (1 < or = p < or = infinity); for example, the linear approximation problem and both the minimax and minisum problems of location theory. Convergence of the algorithm to an epsilon - optimal solution is proved and its effectiveness demonstrated by solving a number of problems from location theory and linear approximation theory. Our computational results are compared with other solution methods.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1977
Accession Number
ADA050166

Entities

People

  • Donald Hearn
  • Jacques Chatelon
  • Timothy J. Lowe

Organizations

  • University of Florida

Tags

Communities of Interest

  • Ground and Sea Platforms

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Center Of Gravity
  • Computations
  • Convergence
  • Convex Sets
  • Direction Finding
  • Directional
  • Engineering
  • Inequalities
  • Iterations
  • Military Research
  • Numbers
  • Sequences
  • Stationary
  • Systems Engineering
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Operations Research