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Convexity of Quadratic Transformations and Its Use in Control and Optimization

Citations

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Cited by:

  1. M. Ruiz Galán, 2017. "A theorem of the alternative with an arbitrary number of inequalities and quadratic programming," Journal of Global Optimization, Springer, vol. 69(2), pages 427-442, October.
  2. Shenglong Hu & Guoyin Li & Liqun Qi, 2016. "A Tensor Analogy of Yuan’s Theorem of the Alternative and Polynomial Optimization with Sign structure," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 446-474, February.
  3. Gabriel Haeser, 2017. "An Extension of Yuan’s Lemma and Its Applications in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 641-649, September.
  4. Sheng-Long Hu & Zheng-Hai Huang, 2012. "Theorems of the Alternative for Inequality Systems of Real Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 1-16, July.
  5. Guoyin Li, 2012. "Global Quadratic Minimization over Bivalent Constraints: Necessary and Sufficient Global Optimality Condition," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 710-726, March.
  6. Fabián Flores-Bazán & William Echegaray & Fernando Flores-Bazán & Eladio Ocaña, 2017. "Primal or dual strong-duality in nonconvex optimization and a class of quasiconvex problems having zero duality gap," Journal of Global Optimization, Springer, vol. 69(4), pages 823-845, December.
  7. C. Durieu & É. Walter & B. Polyak, 2001. "Multi-Input Multi-Output Ellipsoidal State Bounding," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 273-303, November.
  8. de Klerk, E., 2006. "The Complexity of Optimizing over a Simplex, Hypercube or Sphere : A Short Survey," Other publications TiSEM 88640b6d-5240-472d-8669-4, Tilburg University, School of Economics and Management.
  9. Huu-Quang Nguyen & Ruey-Lin Sheu, 2019. "Geometric properties for level sets of quadratic functions," Journal of Global Optimization, Springer, vol. 73(2), pages 349-369, February.
  10. B. S. Mordukhovich & M. E. Sarabi, 2017. "Stability Analysis for Composite Optimization Problems and Parametric Variational Systems," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 554-577, February.
  11. de Klerk, E., 2006. "The Complexity of Optimizing over a Simplex, Hypercube or Sphere : A Short Survey," Discussion Paper 2006-85, Tilburg University, Center for Economic Research.
  12. Immanuel Bomze & Markus Gabl, 2021. "Interplay of non-convex quadratically constrained problems with adjustable robust optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(1), pages 115-151, February.
  13. A. Beck, 2009. "Convexity Properties Associated with Nonconvex Quadratic Matrix Functions and Applications to Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 1-29, July.
  14. H. Tuy & H. Tuan, 2013. "Generalized S-Lemma and strong duality in nonconvex quadratic programming," Journal of Global Optimization, Springer, vol. 56(3), pages 1045-1072, July.
  15. de Klerk, E., 2008. "The complexity of optimizing over a simplex, hypercube or sphere : A short survey," Other publications TiSEM 485b6860-cf1d-4cad-97b8-2, Tilburg University, School of Economics and Management.
  16. A. Baccari & B. Samet, 2009. "An Extension of Polyak’s Theorem in a Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 409-418, March.
  17. V. Jeyakumar & G. Li, 2013. "Robust solutions of quadratic optimization over single quadratic constraint under interval uncertainty," Journal of Global Optimization, Springer, vol. 55(2), pages 209-226, February.
  18. Meijia Yang & Shu Wang & Yong Xia, 2022. "Toward Nonquadratic S-Lemma: New Theory and Application in Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 353-363, July.
  19. Yongwei Huang & Shuzhong Zhang, 2007. "Complex Matrix Decomposition and Quadratic Programming," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 758-768, August.
  20. Wenbao Ai & Yongwei Huang & Shuzhong Zhang, 2008. "On the Low Rank Solutions for Linear Matrix Inequalities," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 965-975, November.
  21. Zhuoyi Xu & Linbin Li & Yong Xia, 2023. "A partial ellipsoidal approximation scheme for nonconvex homogeneous quadratic optimization with quadratic constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 93-109, August.
  22. J. B. Lasserre & J. B. Hiriart-Urruty, 2002. "Mathematical Properties of Optimization Problems Defined by Positively Homogeneous Functions," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 31-52, January.
  23. Etienne Klerk, 2008. "The complexity of optimizing over a simplex, hypercube or sphere: a short survey," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 111-125, June.
  24. Mengmeng Song & Yong Xia, 2023. "Calabi-Polyak convexity theorem, Yuan’s lemma and S-lemma: extensions and applications," Journal of Global Optimization, Springer, vol. 85(3), pages 743-756, March.
  25. NESTEROV, Yurii & POLYAK, Boris, 2003. "Cubic regularization of a Newton scheme and its global performance," LIDAM Discussion Papers CORE 2003041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  26. Qingzhi Yang & Yang Zhou & Yuning Yang, 2019. "An Extension of Yuan’s Lemma to Fourth-Order Tensor System," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 803-810, March.
  27. Gulcin Dinc Yalcin & Refail Kasimbeyli, 2020. "On weak conjugacy, augmented Lagrangians and duality in nonconvex optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(1), pages 199-228, August.
  28. Van-Bong Nguyen & Thi Ngan Nguyen & Ruey-Lin Sheu, 2020. "Strong duality in minimizing a quadratic form subject to two homogeneous quadratic inequalities over the unit sphere," Journal of Global Optimization, Springer, vol. 76(1), pages 121-135, January.
  29. Kürşad Derinkuyu & Mustafa Pınar, 2006. "On the S-procedure and Some Variants," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 55-77, August.
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