A Secure Revised Simplex Algorithm for Privacy-Preserving Linear Programming

2009 ◽  
Author(s):  
Jaideep Vaidya
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm ◽  
Privacy Preserving ◽  
Revised Simplex Algorithm

Revised simplex algorithm for linear programming on GPUs with CUDA

2018 ◽  
Vol 77 (22) ◽  
pp. 30035-30050 ◽  
Author(s):  
Lili He ◽  
Hongtao Bai ◽  
Yu Jiang ◽  
Dantong Ouyang ◽  
Shanshan Jiang
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm ◽  
Revised Simplex Algorithm

A Decision Support System for Solving Linear Programming Problems

2014 ◽  
Vol 6 (2) ◽  
pp. 46-62
Author(s):  
Nikolaos Ploskas ◽  
Nikolaos Samaras ◽  
Jason Papathanasiou
Keyword(s):  
Linear Programming ◽  
Decision Support ◽  
Simplex Algorithm ◽  
Decision Makers ◽  
Web Interface ◽  
Web Based ◽  
Linear Programming Problems ◽  
Revised Simplex Algorithm ◽  
The Given ◽  
Programming Algorithms

Linear programming algorithms have been widely used in Decision Support Systems. These systems have incorporated linear programming algorithms for the solution of the given problems. Yet, the special structure of each linear problem may take advantage of different linear programming algorithms or different techniques used in these algorithms. This paper proposes a web-based DSS that assists decision makers in the solution of linear programming problems with a variety of linear programming algorithms and techniques. Two linear programming algorithms have been included in the DSS: (i) revised simplex algorithm and (ii) exterior primal simplex algorithm. Furthermore, ten scaling techniques, five basis update methods and eight pivoting rules have been incorporated in the DSS. All linear programming algorithms and methods have been implemented using MATLAB and converted to Java classes using MATLAB Builder JA, while the web interface of the DSS has been designed using Java Server Pages.

scholarly journals Optimization of a complex hydropower development operation using HEC-ResSim

2022 ◽  
Vol 1216 (1) ◽  
pp. 012017
Author(s):  
E I Tică ◽  
K Ahmad-Rashid ◽  
O V Sima ◽  
F Popa ◽  
O Nedelcu ◽  
...  
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Energy Generation ◽  
Simplex Algorithm ◽  
Hydropower Development ◽  
Hydropower Plants ◽  
The Mean ◽  
One Year ◽  
Revised Simplex Algorithm

Abstract In this paper HEC-ResSim is applied for a complex hydropower development formed by five reservoirs and related hydropower plants. There were considered characteristics of five existing hydropower developments in Romania, for which three reservoirs are with annual regulation and two with daily regulation. The objective function was the realization of a planned energy generation for one year (the mean hydrological year). Obtained results are very close to those obtained applying linear programming, a revised simplex algorithm.

scholarly journals Verifying a Solver for Linear Mixed Integer Arithmetic in Isabelle/HOL

2020 ◽  
pp. 233-250
Author(s):  
Ralph Bottesch ◽  
Max W. Haslbeck ◽  
Alban Reynaud ◽  
René Thiemann
Keyword(s):  
Linear Programming ◽  
Branch And Bound ◽  
Decision Procedure ◽  
Simplex Algorithm ◽  
Upper Bounds ◽  
Mixed Integer ◽  
Small Solution ◽  
Code Generator ◽  
Integer Arithmetic ◽  
Termination Proofs

AbstractWe implement a decision procedure for linear mixed integer arithmetic and formally verify its soundness in Isabelle/HOL. We further integrate this procedure into one application, namely into , a formally verified certifier to check untrusted termination proofs. This checking involves assertions of unsatisfiability of linear integer inequalities; previously, only a sufficient criterion for such checks was supported. To verify the soundness of the decision procedure, we first formalize the proof that every satisfiable set of linear integer inequalities also has a small solution, and give explicit upper bounds. To this end we mechanize several important theorems on linear programming, including statements on integrality and bounds. The procedure itself is then implemented as a branch-and-bound algorithm, and is available in several languages via Isabelle’s code generator. It internally relies upon an adapted version of an existing verified incremental simplex algorithm.

scholarly journals A Monotonic Build-Up Simplex Algorithm for Linear Programming

1994 ◽  
Vol 42 (3) ◽  
pp. 556-561 ◽  
Author(s):  
Kurt M. Anstreicher ◽  
Tamás Terlaky
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm

Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables

2013 ◽  
pp. 64-82
Author(s):  
Seyed Hadi Nasseri ◽  
Ali Ebrahimnejad
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm ◽  
Programming Models ◽  
Fuzzy Data ◽  
Fuzzy Variables ◽  
Fuzzy Environment ◽  
Dual Simplex ◽  
Linear Programming Problems ◽  
Simplex Tableau ◽  
Dual Simplex Algorithm

In the real word, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables. Some authors considered these problems and have developed various methods for solving these problems. Recently, Mahdavi-Amiri and Nasseri (2007) considered linear programming problems with trapezoidal fuzzy data and/or variables and stated a fuzzy simplex algorithm to solve these problems. Moreover, they developed the duality results in fuzzy environment and presented a dual simplex algorithm for solving linear programming problems with trapezoidal fuzzy variables. Here, the authors show that this presented dual simplex algorithm directly using the primal simplex tableau algorithm tenders the capability for sensitivity (or post optimality) analysis using primal simplex tableaus.

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