Open Access
RAIRO-Oper. Res.
Volume 56, Number 3, May-June 2022
Page(s) 1353 - 1371
Published online 02 June 2022
  • F. Ahmed, M. Dür and G. Still, Copositive Programming via semi-infinite optimization. J. Optim. Theory Appl. 159 (2013) 322–340. [CrossRef] [MathSciNet] [Google Scholar]
  • M.F. Anjos, J.B. Lasserre (editors), Handbook of Semidefinite, Conic and Polynomial Optimization. International Series in Operational Research and Management Science. Vol. 166. Springer US (2012) 138. [Google Scholar]
  • I.M. Bomze, Copositive optimization – recent developments and applications. EJOR 216 (2012) 509–520. [CrossRef] [Google Scholar]
  • J.F. Bonnans and A. Shapiro, Perturbation analysis of optimization problems. Springer-Verlag, New-York, NY (2000) 601. [Google Scholar]
  • J.M. Borwein and H. Wolkowicz, Facial reduction for a cone-convex programming problem. J. Austral. Math. Soc. Ser. A. 30 (1981) 369–380. [CrossRef] [Google Scholar]
  • J.M. Borwein and H. Wolkowicz, Regularizing the abstract convex program. J. Math. Anal. Appl. 83 (1981) 495–530. [CrossRef] [MathSciNet] [Google Scholar]
  • E. de Klerk and D.V. Pasechnik, Approximation of the stability number number of a graph via copositive programming. SIAM J. Optim. 12 (2002) 875–892. [CrossRef] [MathSciNet] [Google Scholar]
  • D. Drusvyatskiy and H. Wolkowicz, The many faces of degeneracy in conic optimization. In: Foundations and Trends in Optimization. Vol. 3. Now Publishers Inc. (2017) 77–170. [CrossRef] [Google Scholar]
  • M. Dür, Copositive programming – a survey. In: Recent Advances in Optimization and its Applications in Engineering, edited by M. Diehl, F. Glineur, E. Jarlebring and W. Michielis. Springer-Verlag, Berlin, Heidelberg (2010) 535. [Google Scholar]
  • K.O. Kortanek and Q. Zhang, Perfect duality in semi-infinite and semidefinite programming. Math. Program. Ser. A 91 (2001) 127–144. [CrossRef] [Google Scholar]
  • O.I. Kostyukova and T.V. Tchemisova, Optimality conditions for convex semi-infinite programming problems with finitely representable compact index sets. J. Optim. Theory Appl. 175 (2017) 76–103. [CrossRef] [MathSciNet] [Google Scholar]
  • O.I. Kostyukova and T.V. Tchemisova, On equivalent representations and properties of faces of the cone of copositive matrices. Optimization (2020). DOI: 10.1080/02331934.2022.2027939. [Google Scholar]
  • O. Kostyukova and T. Tchemisova, On strong duality in linear copositive programming. J. Global Optim. (2021) 1–24. DOI: 10.1007/s10898-021-00995-3. [Google Scholar]
  • O.I. Kostyukova, T.V. Tchemisova and O.S. Dudina, Immobile indices and CQ-free optimality criteria for linear copositive programming problems. Set-Valued Var. Anal. 28 (2020) 89–107. [CrossRef] [MathSciNet] [Google Scholar]
  • A.N. Letchford and A.J. Parkes, A guide to conic optimisation and its applications. RAIRO Oper. Res. 52 (2018) 1087–1106. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  • V.L. Levin, Application of E. Helly’s theorem to convex programming, problems of best approximation and related questions. Math. USSR Sbornik 8 (1969) 235–247. [CrossRef] [Google Scholar]
  • Z.-Q. Luo, F.J. Sturm and S. Zhang, Duality Results for Conic Convex Programming, Econometric institute report no. 9719/a. Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute (1997). [Google Scholar]
  • G. Pataki, simple derivation of a facial reduction algorithm and extended dual systems. Preprint available at (2000). [Google Scholar]
  • F. Permenter, H. Friberg and E. Andersen, Solving conic optimization problems via self-dual embedding and facial reduction: a unified approach. Tech. Report. (2015). DOI: 10.13140/RG.2.1.4340.7847. [Google Scholar]
  • I. Pólik and T. Terlaky, Exact Duality for Optimization Over Symmetric Cones. AdvOL-Report No. 2007/10. McMaster University, Advanced Optimization Lab., Hamilton, Canada (2007). [Google Scholar]
  • M.V. Ramana, L. Tuncel and H. Wolkowicz, Strong duality for semidefinite programming. SIAM J. Optim. 7 (1997) 641–662. [CrossRef] [MathSciNet] [Google Scholar]
  • M.V. Solodov, Constraint qualifications. In: Wiley Encyclopedia of Operations Research and Management Science, edited by J.J. Cochran, et al. John Wiley & Sons, Inc. (2010). [Google Scholar]
  • L. Tunçel and H. Wolkowicz, Strong duality and minimal representations for cone optimization. Comput. Optim. Appl. 53 (2013) 619–648. [Google Scholar]
  • H. Waki and M. Muramatsu, Facial reduction algorithms for conic optimization problems. J. Optim. Theory Appl. 158 (2013) 188–215. [CrossRef] [MathSciNet] [Google Scholar]
  • G.-W. Weber, Generalized semi-infinite optimization and related topics. In: Research and Exposition in Mathematics, edited by K.H. Hofmann, R. Willem. Vol. 29. Heldermann Publishing House, Lemgo (2003). [Google Scholar]
  • H. Wolkowicz, R. Saigal and L. Vandenberghe, Handbook of Semidefinite Programming – Theory, Algorithms, and Applications. Kluwer Academic Publishers (2000). [CrossRef] [Google Scholar]

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