|
[1]
|
S. Adachi, S. Iwata, Y. Nakatsukasa and A. Takeda, Solving the trust-region subproblem by a generalized eigenvalue problem, SIAM Journal on Optimization, 27 (2017), 269-291.
doi: 10.1137/16M1058200.
|
|
[2]
|
S. Ansary Karbasy and M. Salahi, A hybrid algorithm for the two-trust-region subproblem, Computational and Applied Mathematics, https://doi.org/10.1007/s40314-019-0864-y
doi: 10.1007/s40314-019-0864-y.
|
|
[3]
|
H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems, Springer Science and Business Media, 2012.
doi: 10.1007/978-1-4612-3700-6.
|
|
[4]
|
A. Beck and Y. C. Eldar, Strong duality in nonconvex quadratic optimization with two quadratic constraints, SIAM Journal on Optimization, 17 (2006), 844-860.
doi: 10.1137/050644471.
|
|
[5]
|
Im. Bomze and Ml. Overton, Narrowing the difficulty gap for the Celis-Dennis-Tapia problem, Mathematical Programming, 151 (2015), 459-476.
doi: 10.1007/s10107-014-0836-3.
|
|
[6]
|
S. Burer and K. M. Anstreicher, Second-order-cone constraints for extended trust-region subproblems, SIAM Journal on Optimization, 23 (2013), 432-451.
doi: 10.1137/110826862.
|
|
[7]
|
S. Burer and B. Yang, The trust-region subproblem with non-intersecting linear constraints, Mathematical Programming, 149 (2015), 253-264.
doi: 10.1007/s10107-014-0749-1.
|
|
[8]
|
M. R. Celis, J. E. Dennis and R. A. Tapia, A trust-region strategy for nonlinear equality constrained optimization, Numerical Optimization, (1984), 71–82.
|
|
[9]
|
A. R. Conn, N. I. Gould and P. L. Toint, Trust-Region Methods, SIAM Philadelphia, Vol: 1, 2000.
doi: 10.1137/1.9780898719857.
|
|
[10]
|
J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM publisher, Vol: 16, 1996.
doi: 10.1137/1.9781611971200.
|
|
[11]
|
S. Fallahi, M. Salahi and S. Ansary Karbasy, On SOCP/SDP formulation of the extended trust-region subproblem, to appear in Iranian Journal of Operations Research, 2019.
doi: 10.1007/s40314-019-0864-y.
|
|
[12]
|
M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming, version 2.1, March 2017. Available from: http://cvxr.com/cvx.
|
|
[13]
|
S. Gugercin, A. C. Antoulas and H. P. Zhang, An approach to identification for robust control, IEEE Transactions on Automatic Control, 48 (2003), 1109-1115.
doi: 10.1109/TAC.2003.812821.
|
|
[14]
|
M. Heinkenschloss, Mesh independence for nonlinear least squares problems with norm constraints, SlAM Journal on Optimization, 3 (1993), 81-117.
doi: 10.1137/0803005.
|
|
[15]
|
M. Heinkenschloss, On the solution of a two ball trust-region subproblem, Mathematical Programming, 64 (1994), 249-276.
doi: 10.1007/BF01582576.
|
|
[16]
|
V. Jeyakumar and G. Y. Li, Trust-region problems with linear inequality constraints: Exact SDP relaxation,
global optimality and robust optimization, Mathematical Programming, 147 (2014), 171-206.
doi: 10.1007/s10107-013-0716-2.
|
|
[17]
|
B. Kaltenbacher, F. Rendl and E. Resmerita, Computing quasisolutions of nonlinear inverse problems via efficient minimization of trust region problems, Journal of Inverse and Ill-Posed Problems, 24 (2016), 435-447.
doi: 10.1515/jiip-2015-0087.
|
|
[18]
|
C. Kravaris and J. H. Seinfeld, Identification of parameters in distributed parameter systems by regularization, SIAM Journal on Control and Optimization, 23 (1985), 217-241.
doi: 10.1137/0323017.
|
|
[19]
|
G. Kristensson, Inverse problems for acoustic waves using the penalised likelihood method, Inverse Problems, 2 (1986), 461.
|
|
[20]
|
J. M. Martínez, Local minimizers of quadratic functions on Euclidean balls and spheres, SIAM Journal on Optimization, 4 (1994), 159-176.
doi: 10.1137/0804009.
|
|
[21]
|
Y. Nesterov, H. Wolkowicz and Y. Ye, Semidefinite Programming Relaxations of Nonconvex Quadratic Optimization, Handbook of Semidefinite Programming, Springer, Boston, (2000), 361–419.
doi: 10.1007/978-1-4615-4381-7_13.
|
|
[22]
|
S. Omatu and J. H. Seinfeld, Distributed Parameter Systems: Theory and Applications,, Clarendon Press, 1989.
|
|
[23]
|
F. O'Sullivan and G. Wahba, A cross validated Bayesian retrieval algorithm for nonlinear remote sensing experiments, Journal of Computational Physics, 59 (1985), 441-455.
|
|
[24]
|
J.-M. Peng and Y. Yuan, Optimality conditions for the minimization of a quadratic with two quadratic constraints, SIAM Journal on Optimization, 7 (1997), 579-594.
doi: 10.1137/S1052623494261520.
|
|
[25]
|
S. Sakaue, Y. Nakatsukasa, A. Takeda and S. Iwata, Solving generalized CDT problems via two-parameter eigenvalues, SIAM Journal on Optimization, 26 (2016), 1669-1694.
doi: 10.1137/15100624X.
|
|
[26]
|
M. Salahi and A. Taati, A fast eigenvalue approach for solving the trust-region subproblem with an additional linear inequality, Computational and Applied Mathematics, 37 (2018), 329-347.
doi: 10.1007/s40314-016-0347-3.
|
|
[27]
|
M. Salahi, A. Taati and H. Wolkowicz, Local nonglobal minima for solving large scale extended trust-region subproblems, Computational Optimization and Applications, 66 (2016), 223-244.
doi: 10.1007/s10589-016-9867-4.
|
|
[28]
|
M. Salah and S. Fallahi, Trust-region subproblem with an additional linear inequality constraint, Optimization Letters, 10 (2016), 821-832.
doi: 10.1007/s11590-015-0957-5.
|
|
[29]
|
J. F. Sturm and S. Zhang, On cones of nonnegative quadratic functions, Mathematics of Operations Research, 28 (2003), 246-267.
doi: 10.1287/moor.28.2.246.14485.
|
|
[30]
|
C. R. Vogel, A constrained least squares regularization method for nonlinear iii-posed problems, SIAM Journal on Control and Optimization, 28 (1990), 34-49.
doi: 10.1137/0328002.
|
|
[31]
|
A. Zhang and S. Hayashi, Celis-Dennis-Tapia based approach to quadratic fractional programming problems with two quadratic constraints, Numerical Algebra, Control and Optimization, 1 (2011), 83-98.
doi: 10.3934/naco.2011.1.83.
|
Download:
{{journal.titleEn}} 
