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Volume 15, Issue 4
Finding the Strictly Local and $\epsilon $-Global Minimizers of Concave Minimization with Linear Constraints

Patrice Marcotte & Shiquan Wu

J. Comp. Math., 15 (1997), pp. 327-334.

Published online: 1997-08

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  • Abstract

This paper considers the concave minimization problem with linear constraints, proposes a technique which may avoid the unsuitable Karush-Kuhn-Tucker points, then combines this technique with Frank-Wolfe method and simplex method to form a pivoting method which can determine a strictly local minimizer of the problem in a finite number of iterations. Based on strictly local minimizers, a new cutting plane method is proposed. Under some mild conditions, the new cutting plane method is proved to be finitely terminated at an $\epsilon $-global minimizer of the problem.

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@Article{JCM-15-327, author = {Marcotte , Patrice and Wu , Shiquan}, title = {Finding the Strictly Local and $\epsilon $-Global Minimizers of Concave Minimization with Linear Constraints}, journal = {Journal of Computational Mathematics}, year = {1997}, volume = {15}, number = {4}, pages = {327--334}, abstract = {

This paper considers the concave minimization problem with linear constraints, proposes a technique which may avoid the unsuitable Karush-Kuhn-Tucker points, then combines this technique with Frank-Wolfe method and simplex method to form a pivoting method which can determine a strictly local minimizer of the problem in a finite number of iterations. Based on strictly local minimizers, a new cutting plane method is proposed. Under some mild conditions, the new cutting plane method is proved to be finitely terminated at an $\epsilon $-global minimizer of the problem.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9210.html} }
TY - JOUR T1 - Finding the Strictly Local and $\epsilon $-Global Minimizers of Concave Minimization with Linear Constraints AU - Marcotte , Patrice AU - Wu , Shiquan JO - Journal of Computational Mathematics VL - 4 SP - 327 EP - 334 PY - 1997 DA - 1997/08 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9210.html KW - AB -

This paper considers the concave minimization problem with linear constraints, proposes a technique which may avoid the unsuitable Karush-Kuhn-Tucker points, then combines this technique with Frank-Wolfe method and simplex method to form a pivoting method which can determine a strictly local minimizer of the problem in a finite number of iterations. Based on strictly local minimizers, a new cutting plane method is proposed. Under some mild conditions, the new cutting plane method is proved to be finitely terminated at an $\epsilon $-global minimizer of the problem.

Patrice Marcotte & Shiquan Wu. (1970). Finding the Strictly Local and $\epsilon $-Global Minimizers of Concave Minimization with Linear Constraints. Journal of Computational Mathematics. 15 (4). 327-334. doi:
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