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Complexity and numerical experiments of a new adaptive generic proximal bundle method

Vincent Guigues, Renato Monteiro, Benoit Tran

Abstract

This paper develops an adaptive generic proximal bundle method, shows its complexity, and presents numerical experiments comparing this method with two bundle methods on a set of optimization problems.

Complexity and numerical experiments of a new adaptive generic proximal bundle method

Abstract

This paper develops an adaptive generic proximal bundle method, shows its complexity, and presents numerical experiments comparing this method with two bundle methods on a set of optimization problems.

Paper Structure

This paper contains 14 sections, 5 theorems, 38 equations, 7 tables.

Table of Contents

  1. Introduction
  2. Adaptive GPB
  3. Bundle update blackbox
  4. Adaptive GPB subroutine
  5. Main loop of Adaptive GPB
  6. Complexity analysis
  7. Numerical experiments
  8. BadGuy
  9. Chained CB3 II
  10. MaxQuad
  11. MXHILB
  12. RandMaxQuad
  13. TiltedNorm
  14. Conclusion

Key Result

Lemma 3.1

Define $\varepsilon=\bar{\varepsilon}/2$ and $\lambda_*$ by i.e., Then the following holds for Adaptive GPB:

Theorems & Definitions (9)

  • Lemma 3.1
  • proof
  • Lemma 3.2
  • Theorem 3.3
  • proof
  • Proposition 3.4
  • proof
  • Theorem 3.5
  • proof