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Partial Exactness for the Penalty Function of Biconvex Programming.

Min Jiang1, Zhiqing Meng1, Rui Shen2

  • 1School of Management, Zhejiang University of Technology, Hangzhou 310023, China.

Entropy (Basel, Switzerland)
|January 26, 2021
PubMed
Summary
This summary is machine-generated.

This study investigates the partial exactness of penalty functions for biconvex programming. A new algorithm is presented for finding partial optimum solutions in optimization problems.

Keywords:
biconvex programmingpartial exactnesspartial local stabilitypartial optimumpartially exact penalty function

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Area of Science:

  • Optimization Theory
  • Applied Mathematics
  • Computer Science

Background:

  • Biconvex programming is crucial for machine learning and signal processing.
  • Understanding penalty functions is key to solving these optimization problems.

Purpose of the Study:

  • To study the partial exactness of penalty functions in biconvex programming.
  • To establish conditions for partial exactness and develop a novel algorithm.

Main Methods:

  • Analysis of the partial Karush-Kuhn-Tucker (KKT) conditions.
  • Proving sufficient and necessary partially local stability conditions.
  • Developing and proving the convergence of a new penalty function-based algorithm.

Main Results:

  • The partial exactness of the penalty function is defined by the partial KKT condition.
  • A novel condition for partially local stability is identified.
  • A convergent algorithm for finding partial optimum solutions is presented.

Conclusions:

  • The research provides theoretical insights into biconvex programming.
  • The developed algorithm offers a practical approach for optimization problems in engineering and data science.
  • This work contributes to the advancement of optimization techniques.