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Minimax Programs
 University of California Press
, 1997
"... We introduce an optimization problem called a minimax program that is similar to a linear program, except that the addition operator is replaced in the constraint equations by the maximum operator. We clarify the relation of this problem to some betterknown problems. We identify an interesting spec ..."
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Cited by 475 (5 self)
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We introduce an optimization problem called a minimax program that is similar to a linear program, except that the addition operator is replaced in the constraint equations by the maximum operator. We clarify the relation of this problem to some betterknown problems. We identify an interesting
Convergence results of a local minimax method for finding multiple critical points
 SIAM Sci. Comp
"... In [14], a new local minimax method that characterizes a saddle point as a solution to a local minimax problem is established. Based on the local characterization, a numerical minimax algorithm is designed for finding multiple saddle points. Numerical computations of many examples in semilinear elli ..."
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Cited by 18 (9 self)
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In [14], a new local minimax method that characterizes a saddle point as a solution to a local minimax problem is established. Based on the local characterization, a numerical minimax algorithm is designed for finding multiple saddle points. Numerical computations of many examples in semilinear
Consolidation of a WSN and Minimax Method to Rapidly Neutralise
 Intruders in Strategic Installations. Sensors 2012
"... sensors ..."
Convergence Results of A Minimax Method for Finding Multiple Critical Points
 SIAM J. Sci. Comp
"... In [12], new local minimax theorems which characterize a saddle point as a solution toatwolevellocal minimax problem are established. Based on the local characterization, a numerical minimax method is designed for finding multiple saddle points. Many numerical examples in semilinear elliptic PDE ha ..."
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Cited by 8 (6 self)
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In [12], new local minimax theorems which characterize a saddle point as a solution toatwolevellocal minimax problem are established. Based on the local characterization, a numerical minimax method is designed for finding multiple saddle points. Many numerical examples in semilinear elliptic PDE
Instability Analysis of Saddle Points by a Local Minimax Method
 Math. Comp
"... Abstract. The objective of this work is to develop some tools for local instability analysis of multiple critical points, which can be computationally carried out. The Morse index can be used to measure local instability of a nondegenerate saddle point. However, it is very expensive to compute numer ..."
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Cited by 11 (9 self)
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local minimax method. This new instability index is known beforehand and can help in finding a saddle point numerically. Relations between the local minimax index and other local instability indices are established. Those relations also provide ways to numerically compute the Morse, local linking
Minimax Estimation via Wavelet Shrinkage
, 1992
"... We attempt to recover an unknown function from noisy, sampled data. Using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coe cients. The shrinkage can be tuned to be nearly minim ..."
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Cited by 322 (32 self)
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minimax over any member of a wide range of Triebel and Besovtype smoothness constraints, and asymptotically minimax over Besov bodies with p q. Linear estimates cannot achieve even the minimax rates over Triebel and Besov classes with p <2, so our method can signi cantly outperform every linear
A Minimax Method With Application To The Initial Vector Coding Problem
, 1993
"... . We consider the problem Minimize max ff 1 (x); : : : ; f m (x)g x 2\Omega where f 1 ; : : : ; f m : IR n ! IR are (generally nonlinear) differentiable functions,\Omega ae IR n and n; m can be large. We introduce a new algorithm for solving this problem that can be implemented in rather mo ..."
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be an effective tool for solving initial vector coding problems. Key words: minimax methods, initial vector coding problem. C.R. Categories: G.2, J.2 Campinas, November 9, 1993. 0 () Work supported by FAPESP (Grants 9037246 and 9124413), FINEP, CNPq and FAEPUNICAMP 0 () Department of Applied Mathematics
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 496 (2 self)
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. This paper studies a method called convex relaxation, which attempts to recover the ideal sparse signal by solving a convex program. This approach is powerful because the optimization can be completed in polynomial time with standard scientific software. The paper provides general conditions which ensure
Adapting to unknown smoothness via wavelet shrinkage
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1995
"... We attempt to recover a function of unknown smoothness from noisy, sampled data. We introduce a procedure, SureShrink, which suppresses noise by thresholding the empirical wavelet coefficients. The thresholding is adaptive: a threshold level is assigned to each dyadic resolution level by the princip ..."
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Cited by 990 (20 self)
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also; if the unknown function has a smooth piece, the reconstruction is (essentially) as smooth as the mother wavelet will allow. The procedure is in a sense optimally smoothnessadaptive: it is nearminimax simultaneously over a whole interval of the Besov scale; the size of this interval depends
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 649 (21 self)
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An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable
Results 1  10
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