Free Access
RAIRO-Oper. Res.
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Page(s) S2905 - S2922
Published online 02 March 2021
  • S. Adachi and Y. Nakatsukasa, Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint. Math. Program. 173 (2019) 79–116. [Google Scholar]
  • S. Adachi, S. Iwata, Y. Nakatsukasa and A. Takeda, Solving the trust region subproblem by a generalized eigenvalue problem. SIAM J. Optim. 27 (2017) 269–291. [Google Scholar]
  • F. Alizadeh and D. Goldfarb, Second-order cone programming. Math. Program. 95 (2003) 3–51. [Google Scholar]
  • W. Ai and S. Zhang, Strong duality for the CDT subproblem: a necessary and sufficient condition. SIAM J. Optim. 19 (2009) 1735–1756. [Google Scholar]
  • S. Ansary Karbasy and M. Salahi, Quadratic optimization with two ball constraints. Numer. Algebra Control Optim. 10 (2020) 165–175. [Google Scholar]
  • A. Beck and Y.C. Eldar, Strong duality in nonconvex quadratic optimization with two quadratic constraints. SIAM J. Optim. 17 (2006) 844–860. [Google Scholar]
  • A. Ben-Tal and D. den Hertog, Hidden conic quadratic representation of some nonconvex quadratic optimization problems. Math. Program. 143 (2014) 1–29. [Google Scholar]
  • A. Ben-Tal and M. Teboulle, Hidden convexity in some nonconvex quadratically constrained quadratic programming. Math. Program. 72 (1996) 51–63. [Google Scholar]
  • D. Bienstock, A note on polynomial solvability of the CDT problem. SIAM J. Optim. 26 (2016) 488–498. [Google Scholar]
  • P.T. Boggs and J.W. Tolle, Sequential quadratic programming. Acta Numer. 4 (1995) 1–51. [Google Scholar]
  • I.M. Bomze and M.L. Overton, Narrowing the difficulty gap for the Celis–Dennis–Tapia problem. Math. Program. 151 (2015) 459–476. [Google Scholar]
  • I.M. Bomze, V. Jeyakumar and G. Li, Extended trust-region problems with one or two balls: exact copositive and Lagrangian relaxations. J. Global Optim. 71 (2018) 551–569. [Google Scholar]
  • M.R. Celis, J.E. Dennis and R.A. Tapia, A trust region strategy for nonlinear equality constrained optimization, edited by P.T. Boggs, R.H. Byrd and R.B. Schnabel. In: Numerical Optimization. SIAM, Philadelphia (1985) 71–82. [Google Scholar]
  • X.-D. Chen and Y.-X. Yuan, On local solutions of the Celis–Dennis–Tapia subproblem. SIAM J. Optim. 10 (1999) 359–383. [Google Scholar]
  • A.R. Conn, N.I.M. Gould and P.L. Toint, Trust Region Methods. SIAM, Philadelphia, PA (2000). [Google Scholar]
  • J.M. Feng, G.X. Lin, R.L. Sheu and Y. Xia, Duality and solutions for quadratic programming over single non-homogeneous quadratic constraint. J. Global Optim. 54 (2012) 275–293. [Google Scholar]
  • G.C. Fehmers, L.P.J. Kamp and F.W. Sluijter, An algorithm for quadratic optimization with one quadratic constraint and bounds on the variables. Inverse Prob. 14 (1998) 893–901. [Google Scholar]
  • C. Fortin and H. Wolkowicz, The trust region subproblem and semidefinite programming. Optim. Methods Softw. 19 (2004) 41–67. [Google Scholar]
  • G.H. Golub and U. Von Matt, Quadratically constrained least squares and quadratic problems. Numer. Math. 59 (1991) 186–197. [Google Scholar]
  • N.I. Gould, S. Lucidi, M. Roma and P.L. Toint, Solving the trust-region subproblem using the Lanczos method. SIAM J. Optim. 9 (1999) 504–525. [Google Scholar]
  • M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming, version 2.1. (2014) 21–57. [Google Scholar]
  • N. Ho-Nguyen and F. Kilinç-Karzan, A Second-order cone based approach for solving the trust-region subproblem and its variants. SIAM J. Optim. 27 (2017) 1485–1512. [Google Scholar]
  • Y. Hsia and R.L. Sheu, Trust region subproblem with a fixed number of additional linear inequality constraints has polynomial complexity. Preprint arXiv:1312.1398 (2013). [Google Scholar]
  • Y. Hsia, G.-X. Lin and R.-L. Sheu, A revisit to quadratic programming with one inequality quadratic constraint via matrix pencil. Pac. J. Optim. 10 (2014) 461–481. [Google Scholar]
  • V. Jeyakumar and G. Li, Strong duality in robust convex programming: complete characterizations. SIAM J. Optim. 20 (2010) 3384–3407. [Google Scholar]
  • V. Jeyakumar and G. Li, A robust von-Neumann minimax theorem for zero-sum games under bounded payoff uncertainty. Oper. Res. Lett. 39 (2011) 109–114. [Google Scholar]
  • V. Jeyakumar and G.Y. Li, Trust-region problems with linear inequality constraints: exact SDP relaxation, global optimality and robust optimization. Math. Program. 147 (2014) 171–206. [Google Scholar]
  • R. Jiang and D. Li, Simultaneous diagonalization of matrices and its applications in quadratically constrained quadratic programming, SIAM J. Optim. 26 (2016) 1649–1668. [Google Scholar]
  • R. Jiang and D. Li, Novel reformulations and efficient algorithms for the generalized trust region subproblem. SIAM J. Optim. 29 (2019) 1603–1633. [Google Scholar]
  • R. Jiang, D. Li and B. Wu, SOCP reformulation for the generalized trust region subproblem via a canonical form of two symmetric matrices. Math. Program. 169 (2018) 531–563. [Google Scholar]
  • P. Lancaster and L. Rodman, Canonical forms for hermitian matrix pairs under strict equivalence and congruence. SIAM Rev. 47 (2005) 407–443. [Google Scholar]
  • M. Locatelli, Some results for quadratic problems with one or two quadratic constraints. Oper. Res. Lett. 43 (2015) 126–131. [Google Scholar]
  • M. Locatelli, Exactness conditions for an SDP relaxation of the extended trust region problem. Optim. Lett. 10 (2016) 1141–1151. [Google Scholar]
  • J.J. Moré, Generalizations of the trust region problem. Optim. Methods Softw. 2 (1993) 189–209. [Google Scholar]
  • J.J. Moré and D.C. Sorensen, Computing a trust region step. SIAM J. Sci. Stat. Comput. 4 (1983) 553–572. [Google Scholar]
  • S. Omatu and J.H. Seinfeld, Distributed Parameter Systems: Theory and Applications. Clarendon Press (1989). [Google Scholar]
  • T. K. Pong and H. Wolkowicz, The generalized trust region subproblem. Comput. Optim. App. 58 (2014) 273–322. [Google Scholar]
  • M.J.D. Powell and Y. Yuan, A trust region algorithm for equality constrained optimization. Math. Program. 49 (1991) 189–211. [Google Scholar]
  • M. Rojas, S.A. Santos and D.C. Sorensen, A new matrix-free algorithm for the large-scale trust-region subproblem. SIAM J. Optim. 11 (2001) 611–646. [Google Scholar]
  • S. Sakaue, Y. Nakatsukasa, A. Takeda and S. Iwata, Solving generalized CDT problems via two-parameter eigenvalues. SIAM J. Optim. 26 (2016) 1669–1694. [Google Scholar]
  • M. Salahi and A. Taati, An efficient algorithm for solving the generalized trust region subproblem. Comput. Appl. Math. 37 (2018) 395–413. [Google Scholar]
  • M. Salahi and A. Taati, A fast eigenvalue approach for solving the trust region subproblem with an additional linear inequality. Comput. Appl. Math. 37 (2018) 329–347. [Google Scholar]
  • M. Salahi, A. Taati and H. Wolkowicz, Local nonglobal minima for solving large-scale extended trust-region subproblems. Comput. Optim. App. 66 (2017) 223–244. [Google Scholar]
  • J.F. Sturm and S. Zhang, On cones of nonnegative quadratic functions. Math. Oper. Res. 28 (2003) 246–267. [Google Scholar]
  • A. Taati and M. Salahi, A conjugate gradient-based algorithm for large-scale quadratic programming problem with one quadratic constraint. Comput. Optim. App. 74 (2019) 195–223. [Google Scholar]
  • A. Taati and M. Salahi, On local non-global minimizers of quadratic optimization problem with a single quadratic constraint. Numer. Funct. Anal. Optim. 41 (2020) 969–1005. [Google Scholar]
  • A.L. Wang and F. Kilinç-Karzan, On the tightness of SDP relaxations of QCQPs. Technical Report, arXiv:1911.09195 (2019). [Google Scholar]
  • Y. Ye and S. Zhang, New results on quadratic minimization. SIAM J. Optim. 14 (2003) 245–267. [Google Scholar]
  • Y. Yuan, On a subproblem of trust region algorithms for constrained optimization. Math. Program. 47 (1990) 53–63. [Google Scholar]
  • Y. Yuan, A dual algorithm for minimizing a quadratic function with two quadratic constraints. J. Comput. Math. 9 (1991) 348–359. [Google Scholar]
  • Y. Zhang, Computing a Celis–Dennis–Tapia trust-region step for equality constrained optimization. Math. Program. 55 (1992) 109–124. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.