Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 1: Variational Analysis, Optimization and Optimal Control. Guest editors: Der-Chen Chang, Robert P. Gilbert, Yongzhi Steve Xu and Jen-Chih Yao
Submit an article Journal homepage
237
Views
18
CrossRef citations to date
0
Altmetric
Articles

A new class of alternative theorems for SOS-convex inequalities and robust optimization

V. JeyakumarDepartment of Applied Mathematics, University of New South Wales, Sydney2052, Australia.Correspondence[email protected]
&
G. LiDepartment of Applied Mathematics, University of New South Wales, Sydney2052, Australia.
Pages 56-74 | Received 18 Jul 2013, Accepted 17 Oct 2013, Published online: 25 Nov 2013

Citations (18)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (3)

La Huang, Ya-Ping Fang & Dan-Yang Liu. (2023) Robust error bounds for uncertain convex inequality systems with applications. Applicable Analysis 102:11, pages 3110-3127.
Read now
Haibin Chen, Liqun Qi, Yiju Wang & Guanglu Zhou. (2022) Further results on sum-of-squares tensors. Optimization Methods and Software 37:1, pages 387-403.
Read now
Linh T. H. Nguyen. (2018) DC approach to weakly convex optimization and nonconvex quadratic optimization problems. Optimization 67:2, pages 195-216.
Read now

Articles from other publishers (15)

Vaithilingam Jeyakumar, Gue Myung Lee, Jae Hyoung Lee & Yingkun Huang. (2023) Sum-of-Squares Relaxations in Robust DC Optimization and Feature Selection. Journal of Optimization Theory and Applications 200:1, pages 308-343.
Crossref
La Huang, Danyang Liu & Yaping Fang. (2022) Convergence of an SDP hierarchy and optimality of robust convex polynomial optimization problems. Annals of Operations Research 320:1, pages 33-59.
Crossref
Liguo Jiao, Jae Hyoung Lee, Yuto Ogata & Tamaki Tanaka. (2020) Multi-objective Optimization Problems with SOS-convex Polynomials over an LMI Constraint. Taiwanese Journal of Mathematics 24:4.
Crossref
Liguo Jiao, Jae Hyoung Lee & Yuying Zhou. (2020) A hybrid approach for finding efficient solutions in vector optimization with SOS-convex polynomials. Operations Research Letters 48:2, pages 188-194.
Crossref
Jae Hyoung Lee & Liguo Jiao. (2019) Finding Efficient Solutions for Multicriteria Optimization Problems with SOS-convex Polynomials. Taiwanese Journal of Mathematics 23:6.
Crossref
N. H. Chieu, J. W. Feng, W. Gao, G. Li & D. Wu. (2017) SOS-Convex Semialgebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization. Set-Valued and Variational Analysis 26:2, pages 305-326.
Crossref
Jae Hyoung Lee & Gue Myung Lee. (2017) On minimizing difference of a SOS-convex polynomial and a support function over a SOS-concave matrix polynomial constraint. Mathematical Programming 169:1, pages 177-198.
Crossref
Jae Hyoung Lee & Liguo Jiao. (2018) Solving Fractional Multicriteria Optimization Problems with Sum of Squares Convex Polynomial Data. Journal of Optimization Theory and Applications 176:2, pages 428-455.
Crossref
Thai Doan Chuong. (2017) Robust alternative theorem for linear inequalities with applications to robust multiobjective optimization. Operations Research Letters 45:6, pages 575-580.
Crossref
Vaithilingam Jeyakumar & Guoyin Li. (2016) Exact Conic Programming Relaxations for a Class of Convex Polynomial Cone Programs. Journal of Optimization Theory and Applications 172:1, pages 156-178.
Crossref
V. Jeyakumar, S. Kim, G. M. Lee & G. Li. (2015) Semidefinite programming relaxation methods for global optimization problems with sparse polynomials and unbounded semialgebraic feasible sets. Journal of Global Optimization 65:2, pages 175-190.
Crossref
V. Jeyakumar, G. M. Lee & N. T. H. Linh. (2015) Generalized Farkas’ lemma and gap-free duality for minimax DC optimization with polynomials and robust quadratic optimization. Journal of Global Optimization 64:4, pages 679-702.
Crossref
M.A. Goberna, V. Jeyakumar, G. Li & N. Linh. (2016) Radius of robust feasibility formulas for classes of convex programs with uncertain polynomial constraints. Operations Research Letters 44:1, pages 67-73.
Crossref
V. Jeyakumar & G. Li. (2015) A bilevel Farkas lemma to characterizing global solutions of a class of bilevel polynomial programs. Operations Research Letters 43:4, pages 405-410.
Crossref
N. Dinh & V. Jeyakumar. (2014) Farkas’ lemma: three decades of generalizations for mathematical optimization. TOP 22:1, pages 1-22.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.