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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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A globally convergent QP-free algorithm for nonlinear semidefinite programming.

Jian-Ling Li1, Zhen-Ping Yang1, Jin-Bao Jian2

  • 1College of Mathematics and Information Science, Guangxi University, Daxue Road 100, Nanning, Guangxi 530004 China.

Journal of Inequalities and Applications
|July 7, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces a new QP-free algorithm for nonlinear semidefinite programming. The method uses a penalty function and Armijo line search for global convergence in optimization problems.

Keywords:
KKT conditionsQP-free algorithmglobal convergencenonlinear semidefinite programmming

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Area of Science:

  • Optimization
  • Nonlinear Programming
  • Semidefinite Programming

Background:

  • Nonlinear semidefinite programming (NSP) is a challenging field in optimization.
  • Existing methods often rely on solving quadratic programming (QP) subproblems.
  • Efficient algorithms are needed for complex NSP problems.

Purpose of the Study:

  • To present a novel QP-free algorithm for solving nonlinear semidefinite programming problems.
  • To demonstrate the global convergence properties of the proposed method.
  • To evaluate the algorithm's performance through preliminary numerical experiments.

Main Methods:

  • A QP-free approach is developed, avoiding the need to solve QP subproblems.
  • The algorithm utilizes a specific penalty function as a merit function for line search.
  • Armijo-type inexact line search is employed to determine the step size at each iteration.

Main Results:

  • The algorithm's search direction is obtained by solving two linear systems with identical coefficient matrices.
  • Global convergence is proven under appropriate theoretical conditions.
  • Initial numerical results indicate the algorithm's potential effectiveness.

Conclusions:

  • The proposed QP-free algorithm offers a viable alternative for nonlinear semidefinite programming.
  • The theoretical convergence guarantees are established.
  • Further numerical studies are warranted to fully assess its practical performance.