SEQUENTIAL MINIMAX SEARCH FOR A ZERO OF A CONVEX FUNCTION

Abstract

Given: a positive and a negative value of a function at two given points respectively. The function is continuous and convex and is otherwise unknown but computable. Starting with this information, a procedure is described for locating its unique root (on the starting interval) within an interval of minimum guaranteeable length in n steps, where a step consists of calculating the value of the function at any point we choose. The pertinent functional equation is derived and curves of the objective function are plotted for n = 1, 2, 3, 4 from data obtained from the Johniac, RAND'S Princeton-type high-speed digital computer.

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Document Details

Document Type
Technical Report
Publication Date
Sep 11, 1956
Accession Number
AD0605086

Entities

People

  • O. Gross
  • S. M. Johnson

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Computations
  • Computer Programming
  • Computers
  • Digital Computers
  • Dynamic Programming
  • Equations
  • Guarantees
  • Hard Copy
  • Intervals
  • Personality
  • Polynomials
  • Standards
  • Test And Evaluation
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Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Approximation Theory.