A Note on Comparing Simplex and Interior Methods for Linear Programming

1989 ◽  
pp. 91-103 ◽  
Author(s):  
J. A. Tomlin
Keyword(s):  
Linear Programming ◽  
Interior Methods

Vector processing in simplex and interior methods for linear programming

1990 ◽  
Vol 22 (1) ◽  
pp. 71-100 ◽  
Author(s):  
J. J. H. Forrest ◽  
J. A. Tomlin
Keyword(s):  
Linear Programming ◽  
Vector Processing ◽  
Interior Methods

Interior methods for constrained optimization

Acta Numerica ◽  
1992 ◽  
Vol 1 ◽  
pp. 341-407 ◽  
Author(s):  
Margaret H. Wright
Keyword(s):  
Linear Programming ◽  
Combinatorial Problems ◽  
Theory And Practice ◽  
Linear Programs ◽  
Great Efficiency ◽  
Barrier Methods ◽  
Interior Method ◽  
Recent Developments ◽  
Interior Methods ◽  
The 1960S

Interior methods for optimization were widely used in the 1960s, primarily in the form of barrier methods. However, they were not seriously applied to linear programming because of the dominance of the simplex method. Barrier methods fell from favour during the 1970s for a variety of reasons, including their apparent inefficiency compared with the best available alternatives. In 1984, Karmarkar's announcement of a fast polynomial-time interior method for linear programming caused tremendous excitement in the field of optimization. A formal connection can be shown between his method and classical barrier methods, which have consequently undergone a renaissance in interest and popularity. Most papers published since 1984 have concentrated on issues of computational complexity in interior methods for linear programming. During the same period, implementations of interior methods have displayed great efficiency in solving many large linear programs of ever-increasing size. Interior methods have also been applied with notable success to nonlinear and combinatorial problems. This paper presents a self-contained survey of major themes in both classical material and recent developments related to the theory and practice of interior methods.

Elementary Linear Programming (2nd edition)

1997 ◽  
Vol 48 (7) ◽  
pp. 757-758
Author(s):  
B Kolman ◽  
R E Beck ◽  
M J Panik
Keyword(s):  
Linear Programming

Robust state estimation in power systems using sparse linear programming

1985 ◽  
Vol 132 (3) ◽  
pp. 123 ◽  
Author(s):  
B.C. Clewer ◽  
M.R. Irving ◽  
M.J.H. Sterling
Keyword(s):  
Linear Programming ◽  
Power Systems ◽  
State Estimation

Optimal approaches to manage power system decarbonation

2020 ◽  
Vol 64 (1-4) ◽  
pp. 1447-1452
Author(s):  
Vincent Mazauric ◽  
Ariane Millot ◽  
Claude Le Pape-Gardeux ◽  
Nadia Maïzi
Keyword(s):  
Free Energy ◽  
Linear Programming ◽  
Phase Transitions ◽  
Power System ◽  
Energy System ◽  
Energy Sources ◽  
Low Carbon ◽  
Faraday’S Law ◽  
Optimal Description ◽  
Low Carbon Technologies

To overcome the negative environemental impact of the actual power system, an optimal description of quasi-static electromagnetics relying on a reversible interpretation of the Faraday’s law is given. Due to the overabundance of carbon-free energy sources, this description makes it possible to consider an evolution towards an energy system favoring low-carbon technologies. The management for changing is then explored through a simplified linear-programming problem and an analogy with phase transitions in physics is drawn.

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