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We consider the fundamental problem of maximizing a general quadratic function over an ellipsoidal domain, also known as the trust region problem.
On general minimax theorems
M. Sion · 1958
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Computing a trust region step
J. J. Moré and D. C. Sorensen · 1983
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A method of solving a convex programming problem with convergence rate O ( 1 / k 2 ) {O}(1/k^{2})
Y. Nesterov · 1983
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A constrained eigenvalue problem
W. Gander, G. H. Golub, and U. von Matt · 1989
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Estimating the largest eigenvalue by the power and lanczos algorithms with a random start
J. Kuczynski and H. Wozniakowski · 1992
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Interior-point polynomial algorithms in convex programming , volume 13
Y. Nesterov, A. S. Nemirovskii, and Y. Ye · 1994
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Interior point methods in semidefinite programming with applications to combinatorial optimization
F. Alizadeh · 1995
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Hidden convexity in some nonconvex quadratically constrained quadratic programming
A. Ben-Tal and M. Teboulle · 1996
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A semidefinite framework for trust region subproblems with applications to large scale minimization
F. Rendl and H. Wolkowicz · 1997
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Minimization of a large-scale quadratic function subject to a spherical constraint
D. Sorensen · 1997
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Solving the trust-region subproblem using the lanczos method
N. I. Gould, S. Lucidi, M. Roma, and P. L. Toint · 1999
Cited alongside, same era.
Trust region methods
A. R. Conn, N. I. Gould, and P. L. Toint · 2000
Cited alongside, same era.
A new matrix-free algorithm for the large-scale trust-region subproblem
M. Rojas, S. A. Santos, and D. C. Sorensen · 2001
Cited alongside, same era.
On cones of nonnegative quadratic functions
J. F. Sturm and S. Zhang · 2003
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Fast algorithms for approximate semidefinite programming using the multiplicative weights update method
S. Arora, E. Hazan, and S. Kale · 2005
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A new trust region technique for the maximum weight clique problem
S. Busygin · 2006
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Computing correlated equilibria in multi-player games
C. H. Papadimitriou and T. Roughgarden · 2008
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A subspace minimization method for the trust-region step
J. B. Erway and P. E. Gill · 2009
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Iterative methods for finding a trust-region step
J. B. Erway, P. E. Gill, and J. D. Griffin · 2009
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On solving trust-region and other regularised subproblems in optimization
N. I. Gould, D. P. Robinson, and H. S. Thorne · 2010
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New results on quadratic minimization
Y. Ye and S. Zhang · 2003
Cited alongside, same era.
A derivative-free algorithm for least-squares minimization
H. Zhang, A. R. Conn, and K. Scheinberg · 2010
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