Linear programming: theory and algorithms

This chapter introduces the concept of maximum dissipation. The elastic set is introduced, and the plastic dissipation is maximized over the elastic set using classical methods from linear programming theory. The plastic flow direction is seen to be generally normal to the yield surface when the plastic dissipation is maximized. The Kuhn-Tucker complementarity conditions are seen in this context to arise from the postulated optimization problem, and the elastic set is seen to be necessarily convex. The concept of maximum dissipation is applied to a Mises material and the models of the earlier chapters are seen to be recovered.

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Applications of linear programming theory to existence and uniqueness classes for the cauchy problem

Annali di Matematica Pura ed Applicata (1923 -) ◽

10.1007/bf02413779 ◽

1977 ◽

Vol 114 (1) ◽

pp. 69-85 ◽

Cited By ~ 1

Author(s):

Stanly Steinberg

Keyword(s):

Cauchy Problem ◽

Linear Programming ◽

Existence And Uniqueness ◽

Programming Theory ◽

The Cauchy Problem

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Support vector machines trained by linear programming: theory and application in image compression and data classification

Proceedings of the 5th Seminar on Neural Network Applications in Electrical Engineering. NEUREL 2000 (IEEE Cat. No.00EX287) ◽

10.1109/neurel.2000.902376 ◽

2002 ◽

Cited By ~ 4

Author(s):

I. Hadzic ◽

V. Kecman

Keyword(s):

Linear Programming ◽

Support Vector Machines ◽

Image Compression ◽

Data Classification ◽

Support Vector ◽

Programming Theory ◽

Vector Machines

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Unbalanced Bidding Model for Bridge Engineering Based on Linear Programming Theory

2015 Sixth International Conference on Intelligent Systems Design and Engineering Applications (ISDEA) ◽

10.1109/isdea.2015.229 ◽

2015 ◽

Author(s):

Yan Jingning ◽

Zhang Yaxian

Keyword(s):

Linear Programming ◽

Bridge Engineering ◽

Programming Theory

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NEWTON FLOW AND INTERIOR POINT METHODS IN LINEAR PROGRAMMING

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127405012363 ◽

2005 ◽

Vol 15 (03) ◽

pp. 827-839 ◽

Cited By ~ 4

Author(s):

JEAN-PIERRE DEDIEU ◽

MIKE SHUB

Keyword(s):

Linear Programming ◽

Vector Field ◽

Interior Point ◽

Barrier Function ◽

Interior Point Methods ◽

Logarithmic Barrier Function ◽

Programming Theory ◽

Central Paths ◽

Logarithmic Barrier

We study the geometry of the central paths of linear programming theory. These paths are the solution curves of the Newton vector field of the logarithmic barrier function. This vector field extends to the boundary of the polytope and we study the main properties of this extension: continuity, analyticity, singularities.

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