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Related Experiment Videos

Primal-dual interior point QP-free algorithm for nonlinear constrained optimization.

Jinbao Jian1, Hanjun Zeng2, Guodong Ma1

  • 1School of Mathematics and Statistics, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, China.

Journal of Inequalities and Applications
|October 17, 2017
PubMed
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A novel QP-free algorithm efficiently solves nonlinear constrained optimization problems using primal-dual interior point methods. This promising approach demonstrates global and superlinear convergence, validated by numerical experiments.

Area of Science:

  • Optimization Theory
  • Numerical Analysis

Background:

  • Nonlinear constrained optimization problems involve complex inequality and equality constraints.
  • Existing methods often rely on quadratic programming (QP) subproblems.

Purpose of the Study:

  • To present a QP-free algorithm for nonlinear constrained optimization.
  • To enhance efficiency and convergence properties of optimization algorithms.

Main Methods:

  • A primal-dual interior point method framework is employed.
  • A simple penalty parameter and a novel working set technique are utilized.
  • The algorithm solves reduced systems of linear equations, relaxing the positive definiteness restriction on the Lagrangian Hessian estimate.

Main Results:

Keywords:
global and superlinear convergenceinequality and equality constraintsoptimizationprimal-dual interior methodworking set

Related Experiment Videos

  • The proposed algorithm achieves global and superlinear convergence under reasonable conditions.
  • Numerical experiments on 59 test problems show promising performance.
  • A modified computation measure for the Lagrangian Hessian estimate is introduced and validated.

Conclusions:

  • The developed QP-free algorithm is effective for nonlinear constrained optimization.
  • The relaxation of the positive definiteness restriction and the new working set technique contribute to improved performance.
  • The algorithm shows significant potential for practical applications in optimization.