article

Convex Separable Minimization Subject to Bounded Variables

Author:

Stefan M. StefanovAuthors Info & Claims

Computational Optimization and Applications, Volume 18, Issue 1

Pages 27 - 48

https://doi.org/10.1023/A:1008739510750

Published: 01 January 2001 Publication History

Abstract

A minimization problem with convex and separable objective function subject to a separable convex inequality constraint “≤” and bounded variables is considered. A necessary and sufficient condition is proved for a feasible solution to be an optimal solution to this problem. Convex minimization problems subject to linear equality/linear inequality “≥” constraint, and bounds on the variables are also considered. A necessary and sufficient condition and a sufficient condition, respectively, are proved for a feasible solution to be an optimal solution to these two problems. Algorithms of polynomial complexity for solving the three problems are suggested and their convergence is proved. Some important forms of convex functions and computational results are given in the Appendix.

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Cited By

Brás CFischer AJúdice JSchönefeld KSeifert S(2017)A block active set algorithm with spectral choice line search for the symmetric eigenvalue complementarity problemApplied Mathematics and Computation10.1016/j.amc.2016.09.005294:C(36-48)Online publication date: 1-Feb-2017
https://dl.acm.org/doi/10.1016/j.amc.2016.09.005
Gao HWang XTang JLiu HRokne JFaloutsos C(2013)Network denoising in social mediaProceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining10.1145/2492517.2492547(564-571)Online publication date: 25-Aug-2013
https://dl.acm.org/doi/10.1145/2492517.2492547
Luna-Ramírez SToril MFernández---Navarro MWille V(2011)Optimal Traffic Sharing in GERANWireless Personal Communications: An International Journal10.1007/s11277-009-9861-657:4(553-574)Online publication date: 1-Apr-2011
https://dl.acm.org/doi/10.1007/s11277-009-9861-6
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Index Terms

Convex Separable Minimization Subject to Bounded Variables
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
      1. Continuous optimization
        Convex optimization
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization
      1. Continuous optimization
        Convex optimization

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Published In

cover image Computational Optimization and Applications

Computational Optimization and Applications Volume 18, Issue 1

Jan. 2001

84 pages

ISSN:0926-6003

Editor:
William W. Hager
Univ. of Florida, USA

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Copyright © Copyright © 2001 Kluwer Academic Publishers.

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Kluwer Academic Publishers

United States

Publication History

Published: 01 January 2001

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Cited By

Brás CFischer AJúdice JSchönefeld KSeifert S(2017)A block active set algorithm with spectral choice line search for the symmetric eigenvalue complementarity problemApplied Mathematics and Computation10.1016/j.amc.2016.09.005294:C(36-48)Online publication date: 1-Feb-2017
https://dl.acm.org/doi/10.1016/j.amc.2016.09.005
Gao HWang XTang JLiu HRokne JFaloutsos C(2013)Network denoising in social mediaProceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining10.1145/2492517.2492547(564-571)Online publication date: 25-Aug-2013
https://dl.acm.org/doi/10.1145/2492517.2492547
Luna-Ramírez SToril MFernández---Navarro MWille V(2011)Optimal Traffic Sharing in GERANWireless Personal Communications: An International Journal10.1007/s11277-009-9861-657:4(553-574)Online publication date: 1-Apr-2011
https://dl.acm.org/doi/10.1007/s11277-009-9861-6
Dahiya KSuneja SVerma V(2007)Convex programming with single separable constraint and bounded variablesComputational Optimization and Applications10.1007/s10589-006-0396-436:1(67-82)Online publication date: 1-Jan-2007
https://dl.acm.org/doi/10.1007/s10589-006-0396-4

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