A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2007; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
A dual version of tardos's algorithm for linear programming

1986
*
Operations Research Letters
*

Abstract Recently, Eva Tardos developed an

doi:10.1016/0167-6377(86)90011-8
fatcat:mffi6k63erfstdw2i545h45mo4
*algorithm*for solving the linear program min(cx: Ax = b, x > O) whose*solution*time is polynomial*in*the size*of*A, independent*of*the sizes*of*c and b. ... Her*algorithm*focuses on the dual*LP*and employs an approximation*of*the cost coefficients. Here we adopt what may be called a 'dual approach'*in*that it focuses on the primal*LP*. ... As such, we can use*Karmarkar's**algorithm*to identify an*optimal*primal*solution*and then use standard techniques to move to an*optimal**basic**solution*. ...##
###
Page 1205 of Mathematical Reviews Vol. , Issue 89B
[page]

1989
*
Mathematical Reviews
*

Szidarovszky (1-AZ-I)
89b:90128 90C05
Kojima, Masakazu (J-TOKYTE-I)

*Determining**basic**variables**of**optimal**solutions**in**Karmarkar’s**new**LP**algorithm*. Algorithmica 1 (1986), no. 4, 499-515. ... A numerical test using the condition is incorporated into*Karmarkar’s**new**LP**algorithm*to*determine*columns*of*an*optimal*basis. ...##
###
Page 3692 of Mathematical Reviews Vol. , Issue 90F
[page]

1990
*
Mathematical Reviews
*

The paper is devoted to the discussion

*of*traditional (the sim- plex method) and*new*(Karmarkar-type*algorithms*) approaches to the*solution**of*large-scale*LP*problems. ... A variant*of**Karmarkar’s*projective*algorithm*for linear program- ming problems*in*which some*variables*are unrestricted is consid- ered. ...##
###
Page 688 of Mathematical Reviews Vol. , Issue 90A
[page]

1990
*
Mathematical Reviews
*

An

*algorithm*is said to be well-behaved on a class D*of**LP*problems if, for each prob- lem*in*D, the computed*solution*, x’, is a slight perturbation*of*the*solution**of*another problem*in*D for which the ... (GR-THRC-E); Vachtsevanos, G. (1-GAIT-E) A*new**algorithm*for the*solution**of*the linear minimax approximation problem.*Optimization*19 (1988), no. 6, 839-860. ...##
###
Page 4759 of Mathematical Reviews Vol. , Issue 89H
[page]

1989
*
Mathematical Reviews
*

Only one artificial

*variable*is needed to*determine*if the linear programming problem has a feasible*solution**in*phase one. ... restrict the choice*of*exiting*basic**variables*. ...##
###
Page 4146 of Mathematical Reviews Vol. , Issue 89G
[page]

1989
*
Mathematical Reviews
*

On the one hand only approximate projections are used

*in**determining*di- rections*of*search and, secondly,*variables*which are likely to be nonbasic are successively eliminated. ...*of*the book contains codes*in**BASIC*for all methods described*in*the text. ...##
###
Progress in mathematical programming

1990
*
European Journal of Operational Research
*

, and that are violated by the

doi:10.1016/0377-2217(90)90262-a
fatcat:gs7on6tmo5ahxnmhx4btkbw6fy
*optimal**solution**of*a*LP*relaxation. ...*Karmarkar's*projective*algorithm*for linear programming provides not only primal*solutions*but dual*solutions*giving bounds on the*optimal*value. ...##
###
Page 5001 of Mathematical Reviews Vol. , Issue 88i
[page]

1988
*
Mathematical Reviews
*

*In*this case, we show the existence

*of*

*basic*feasible

*solutions*and derive a condition for a

*basic*feasible

*solution*to be

*optimal*.” 88i:90121 90C05 Holm, Seren (DK-ODNS) Adding activities to the dual ... An improvement

*in*the bound on the complexity

*of*

*Karmarkar’s*

*algorithm*is proved, namely O(n** log 7). ...

##
###
Page 2722 of Mathematical Reviews Vol. , Issue 88e
[page]

1988
*
Mathematical Reviews
*

Then the extremal flat, where the

*optimal**solutions*are located, is*determined*by the*optimal*value. A feasible*solution*is*optimal*if it satisfies the equation*of*the extremal flat. ... The author is concerned with an*optimality*test for initial*basic*feasible*solutions*for the transportation problem. ...##
###
Page 1619 of Mathematical Reviews Vol. , Issue 87c
[page]

1987
*
Mathematical Reviews
*

*Karmarkar’s*publication does not provide a uniquely

*determined*computational procedure, and also the average case behavior

*of*the

*algorithm*is not clear. ... , where n is the number

*of*

*variables*and L is the number

*of*bits

*in*the input data. ...

##
###
The basic solution ellipsoid method approach for the efficiency measurement problems

2016
*
Lietuvos matematikos rinkinys
*

This paper presents

doi:10.15388/lmr.a.2016.08
fatcat:ealz47ktpjgjpafgdxjnyxakfm
*basic**solution*ellipsoid method approach associated with some problems*of*initial*basic**solution*and the steps*of*it. ... The DEA is a linear programming (*LP*) based technique which deals with the*basic*models (CCR, BCC, SBM, additive)*of*the efficiency evaluation. ... The*solution**of*the problem (1) does not involve any additional*variables*and no*new*conditions for*variable*non-negation are raised, which are often necessary*in*many*of*the*algorithms*for the*solution*...##
###
Introducing Interior-Point Methods for Introductory Operations Research Courses and/or Linear Programming Courses

2009
*
Open Operational Research Journal
*

Consequently, there has been an increasing need to introduce theory and methods

doi:10.2174/1874243200903010001
fatcat:qbdkad3c7bepvijs6m7zjhvgvy
*of*this*new*area*in**optimization*into the appropriate undergraduate and first year graduate courses such as introductory ... Development*of*these methods has quickly led to the design*of**new*and efficient*optimization*codes particularly for Linear Programming. ... However, as*in*the case*of*the Ellipsoid and*Karmarkar's**algorithms*, it can be shown that if the input data are rational numbers, the IPM finds the exact*solution**of**LP**in*O n L ( ) iterations proving ...##
###
INTERIOR POINT ALGORITHM FOR SOLVING FARM RESOURCE ALLOCATION PROBLEM

2017
*
Apstract: Applied Studies in Agribusiness and Commerce
*

Results

doi:10.19041/apstract/2017/1-2/6
fatcat:qcymk7ttijfqzomp5q7wvukcva
*of*the interior point*algorithm*is similar to that*of*the simplex*algorithm*. ... The Simplex*algorithm*saves 39 iterations over Interior Point*algorithm**in*solving the farm resource allocation problem. ... This is done by*determining*the entering*variable*and the outgoing*variable*. An entering*variable*is a*variable*we choose to find*new*BV from a current*basic*feasible*solution*that is not*optimal*. ...##
###
Page 6085 of Mathematical Reviews Vol. , Issue 90J
[page]

1990
*
Mathematical Reviews
*

same set

*of**basic**variables**in*an op- timal*solution*. ... [Elaboration*of*efficient computational setups using*Karmarkar’s**algorithm*]*New*methods*in**optimization*and their industrial uses (Pau/Paris, 1987), 173-190, Internat. Schriftenreihe Numer. ...##
###
A novel method for solving linear programming problems with symmetric trapezoidal fuzzy numbers

2014
*
Applied Mathematical Modelling
*

Linear programming (

doi:10.1016/j.apm.2014.02.024
fatcat:uvxgx44pqjavlmm7z3k4fu326m
*LP*) is a widely used*optimization*method for solving real-life problems because*of*its efficiency. ... We propose a*new*method for solving FLP problems*in*which the coefficients*of*the objective function and the values*of*the right-hand-side are represented by symmetric trapezoidal fuzzy numbers while the ... , it also has an*optimal*fuzzy*basic**solution*. ...
« Previous

*Showing results 1 — 15 out of 199 results*