A Single-Phase Method for Quadratic Programming.

Abstract

This thesis describes a single-phase quadratic programming method useful for solving a sequence of closely-related QP's. One example of this is in the area of nonlinear programming, which uses sequential quadratic programming. Another example is sensitivity analysis involving the constraints. In both of these examples, if the quadratic problems are large-scale and the initial point is infeasible, the single-phase method of this thesis may be particularly useful. If the Hessian is indefinite, the method will find a local minimum when solving a dense QP, and a constrained stationary point when solving a large-scale QP. If the Hessian is positive definite, it will find the global minimum. Additionally, if the QP is known to be positive definite, the method converges more quickly than if the QP were treated as a general indefinite problem. The single-phase method of this thesis is an active-set method which solves a sequence of equality-constraint quadratic programs (EQP). It differs from other active-set methods in that the current iterate may violate constraints in the working set (the prediction of the active set). Special care has been taken to avoid rank deficiency in the working set. An efficient means of solving the successive EQP's of a large-scale problem is included. Finally, an implementation of the method for dense QP's is described.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1985
Accession Number
ADA166373

Entities

People

  • Stephen C. Hoyle

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Computational Science
  • Computations
  • Linear Algebra
  • Linear Programming
  • Mathematical Programming
  • New York
  • Nonlinear Programming
  • Numerical Analysis
  • Operations Research
  • Optimization
  • Quadratic Programming
  • Simplex Method
  • Sparse Matrix
  • Square Roots
  • Systems Engineering
  • Theorems

Readers

  • Operations Research