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Using positive spanning sets to achieve stationarity with the Boosted DC Algorithm

Using positive spanning sets to achieve stationarity with the Boosted DC Algorithm
Using positive spanning sets to achieve stationarity with the Boosted DC Algorithm
The Difference of Convex functions Algorithm (DCA) is widely used for minimizing the difference of two convex functions. A recently proposed accelerated version, termed BDCA for Boosted DC Algorithm, incorporates a line search step to achieve a larger decrease of the objective value at each iteration. Thanks to this step, BDCA usually converges much faster than DCA in practice. The solutions found by DCA are guaranteed to be critical points of the problem, but these may not be local minima. Although BDCA tends to improve the objective value of the solutions it finds, these are frequently just critical
points as well. In this paper we combine BDCA with a simple Derivative-Free Optimization (DFO) algorithm to force the d-stationarity (lack of descent direction) at the point obtained. The potential of this approach is illustrated through some computational experiments on a Minimum-Sum-of-Squares clustering problem. Our numerical results demonstrate that the new method provides better solutions while still remains faster than DCA in the majority of
test cases.
Boosted difference of convex functions algorithm, Derivative-free optimization, Difference of convex functions, Positive spanning sets, d-Stationary points
2305-221X
363-376
Artacho, Francisco J. Aragón
8ab13945-90df-42a6-86f2-51680ad72254
Campoy, Rubén
96dc34f4-f01d-49a2-b1a3-c7c5bc82a213
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Artacho, Francisco J. Aragón
8ab13945-90df-42a6-86f2-51680ad72254
Campoy, Rubén
96dc34f4-f01d-49a2-b1a3-c7c5bc82a213
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf

Artacho, Francisco J. Aragón, Campoy, Rubén and Vuong, Phan Tu (2020) Using positive spanning sets to achieve stationarity with the Boosted DC Algorithm. Vietnam Journal of Mathematics, 48 (2), 363-376. (doi:10.1007/s10013-020-00400-8).

Record type: Article

Abstract

The Difference of Convex functions Algorithm (DCA) is widely used for minimizing the difference of two convex functions. A recently proposed accelerated version, termed BDCA for Boosted DC Algorithm, incorporates a line search step to achieve a larger decrease of the objective value at each iteration. Thanks to this step, BDCA usually converges much faster than DCA in practice. The solutions found by DCA are guaranteed to be critical points of the problem, but these may not be local minima. Although BDCA tends to improve the objective value of the solutions it finds, these are frequently just critical
points as well. In this paper we combine BDCA with a simple Derivative-Free Optimization (DFO) algorithm to force the d-stationarity (lack of descent direction) at the point obtained. The potential of this approach is illustrated through some computational experiments on a Minimum-Sum-of-Squares clustering problem. Our numerical results demonstrate that the new method provides better solutions while still remains faster than DCA in the majority of
test cases.

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1907.11471 - Accepted Manuscript
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Artacho 2020 Article Using Positive Spanning Sets - Version of Record
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More information

Accepted/In Press date: 5 February 2020
e-pub ahead of print date: 30 March 2020
Keywords: Boosted difference of convex functions algorithm, Derivative-free optimization, Difference of convex functions, Positive spanning sets, d-Stationary points

Identifiers

Local EPrints ID: 438483
URI: http://eprints.soton.ac.uk/id/eprint/438483
ISSN: 2305-221X
PURE UUID: 170e0199-5948-4ae7-8c3a-53480f2ca466
ORCID for Phan Tu Vuong: ORCID iD orcid.org/0000-0002-1474-994X

Catalogue record

Date deposited: 11 Mar 2020 17:31
Last modified: 28 Apr 2022 05:31

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Contributors

Author: Francisco J. Aragón Artacho
Author: Rubén Campoy
Author: Phan Tu Vuong ORCID iD

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