Extreme Points and Purification Algorithms in General Linear Programming

1985 ◽  
pp. 123-135 ◽  
Author(s):  
A. S. Lewis
Keyword(s):  
Linear Programming ◽  
Extreme Points ◽  
General Linear

Deconvolution with the ℓ1 norm

Geophysics ◽  
1979 ◽  
Vol 44 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Howard L. Taylor ◽  
Stephen C. Banks ◽  
John F. McCoy
Keyword(s):  
Linear Programming ◽  
Spike Train ◽  
Initial Approximation ◽  
Spike Trains ◽  
General Linear ◽  
Programming System ◽  
Sample Rate ◽  
Weighting Procedures

Given a wavelet w and a noisy trace t + s * w + n, an approximation ŝ of the spike train s can be obtained using the [Formula: see text] norm. This extraction has the advantage of preserving isolated spikes in s. On some types of data the spike train ŝ can represent s as a sparse series of spikes, which may be sampled at a rate higher than the sample rate of the data trace t. The extracted spike train ŝ may be qualitatively much different than those commonly extracted using the [Formula: see text] norm. The [Formula: see text] norm can also be used to extract a wavelet ŵ from a trace t when a spike train s is known. This wavelet extraction can be constrained to give a smooth wavelet which integrates to zero and goes to zero at the ends. Given a trace t and an initial approximation for either s or w, it is possible to alternately extract spike trains and wavelets to improve the representation of trace t. Although special algorithms have been developed to solve [Formula: see text] problems, all of the calculations can be performed using a general linear programming system. Proper weighting procedures allow these methods to be used on ungained data.

scholarly journals Projection-Based Local and Global Lipschitz Moduli of the Optimal Value in Linear Programming

2021 ◽  
Author(s):  
M. J. Cánovas ◽  
M. J. Gisbert ◽  
D. Klatte ◽  
J. Parra
Keyword(s):  
Linear Programming ◽  
Lower Bound ◽  
Value Function ◽  
Extreme Points ◽  
Linear Programs ◽  
Geometrical Approach ◽  
Nominal Data ◽  
Optimal Value ◽  
Lipschitz Modulus ◽  
Finite Linear

AbstractIn this paper, we use a geometrical approach to sharpen a lower bound given in [5] for the Lipschitz modulus of the optimal value of (finite) linear programs under tilt perturbations of the objective function. The key geometrical idea comes from orthogonally projecting general balls on linear subspaces. Our new lower bound provides a computable expression for the exact modulus (as far as it only depends on the nominal data) in two important cases: when the feasible set has extreme points and when we deal with the Euclidean norm. In these two cases, we are able to compute or estimate the global Lipschitz modulus of the optimal value function in different perturbations frameworks.

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