A Secure Revised Simplex Algorithm for Privacy-Preserving Linear Programming

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.

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Optimization of a complex hydropower development operation using HEC-ResSim

IOP Conference Series Materials Science and Engineering ◽

10.1088/1757-899x/1216/1/012017 ◽

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.

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Linear Programming with Mathematica: The Simplex Algorithm

Computational Economics and Finance ◽

10.1007/978-1-4612-2340-5_1 ◽

1996 ◽

pp. 3-30

Author(s):

Michael Carter

Keyword(s):

Linear Programming ◽

Simplex Algorithm

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

Lecture Notes in Computer Science - NASA Formal Methods ◽

10.1007/978-3-030-55754-6_14 ◽

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.

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A Monotonic Build-Up Simplex Algorithm for Linear Programming

Operations Research ◽

10.1287/opre.42.3.556 ◽

1994 ◽

Vol 42 (3) ◽

pp. 556-561 ◽

Cited By ~ 13

Author(s):

Kurt M. Anstreicher ◽

Tamás Terlaky

Keyword(s):

Linear Programming ◽

Simplex Algorithm

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Computing Payoff Allocations in the Approximate Core of Linear Programming Games in a Privacy-Preserving Manner

Operations Research Letters ◽

10.1016/j.orl.2021.12.008 ◽

2021 ◽

Author(s):

George Gilliam ◽

Nelson A. Uhan

Keyword(s):

Linear Programming ◽

Privacy Preserving

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Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables

Optimizing, Innovating, and Capitalizing on Information Systems for Operations ◽

10.4018/978-1-4666-2925-7.ch004 ◽

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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