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Smoothing approximation to the lower order exact penalty function for inequality constrained optimization.

Shujun Lian1, Nana Niu1

  • 1School of Management Science, Qufu Normal University, Rizhao, China.

Journal of Inequalities and Applications
|August 24, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces a novel smoothing method for inequality constrained optimization problems. The new approach efficiently finds approximate global solutions using a smoothed exact penalty function.

Keywords:
Exact penalty functionInequality constrained optimizationLower order penalty functionSmoothing method

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Area of Science:

  • Optimization Theory
  • Numerical Analysis

Background:

  • Inequality constrained optimization problems are prevalent in various scientific and engineering fields.
  • Exact penalty functions are commonly used but often suffer from non-smoothness, complicating solution methods.

Purpose of the Study:

  • To develop a new smoothing technique for lower-order exact penalty functions in inequality constrained optimization.
  • To establish a method for obtaining approximate global solutions to the original problem by solving a smoothed version.

Main Methods:

  • A novel smoothing method is proposed for lower-order exact penalty functions.
  • An algorithm is developed based on the smoothed lower-order exact penalty function.
  • Theoretical analysis is conducted to prove global convergence under mild conditions.

Main Results:

  • The proposed smoothing method transforms the original problem into a smooth one.
  • An approximate global solution to the original problem can be found by solving the smoothed problem.
  • The developed algorithm is proven to have global convergence.

Conclusions:

  • The proposed smoothing method and algorithm are effective for inequality constrained optimization.
  • Numerical experiments demonstrate the efficiency of the new approach.
  • This work provides a valuable tool for solving complex optimization problems.