A Variant of the Dual Simplex Method for a Linear Semidefinite Programming Problem

2017 ◽  
Vol 299 (S1) ◽  
pp. 246-256
Author(s):  
V. G. Zhadan
Keyword(s):  
Semidefinite Programming ◽  
Programming Problem ◽  
Simplex Method ◽  
Dual Simplex Method ◽  
Semidefinite Programming Problem ◽  
Dual Simplex ◽  
Linear Semidefinite Programming

A dual simplex method for grey linear programming problems based on duality results

2020 ◽  
Vol 10 (2) ◽  
pp. 145-157
Author(s):  
Davood Darvishi Salookolaei ◽  
Seyed Hadi Nasseri
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Simplex Method ◽  
Dual Problem ◽  
Complementary Slackness ◽  
Dual Simplex Method ◽  
Content Type ◽  
Dual Simplex ◽  
Linear Programming Problems

PurposeFor extending the common definitions and concepts of grey system theory to the optimization subject, a dual problem is proposed for the primal grey linear programming problem.Design/methodology/approachThe authors discuss the solution concepts of primal and dual of grey linear programming problems without converting them to classical linear programming problems. A numerical example is provided to illustrate the theory developed.FindingsBy using arithmetic operations between interval grey numbers, the authors prove the complementary slackness theorem for grey linear programming problem and the associated dual problem.Originality/valueComplementary slackness theorem for grey linear programming is first presented and proven. After that, a dual simplex method in grey environment is introduced and then some useful concepts are presented.

A Sequential Convex Program Approach to an Inverse Linear Semidefinite Programming Problem

2016 ◽  
Vol 33 (04) ◽  
pp. 1650025 ◽  
Author(s):  
Jia Wu ◽  
Yi Zhang ◽  
Liwei Zhang ◽  
Yue Lu
Keyword(s):  
Semidefinite Programming ◽  
Programming Problem ◽  
Difficult Problem ◽  
Dc Programming ◽  
Convex Program ◽  
Objective Parameter ◽  
Program Approach ◽  
Semidefinite Programming Problem ◽  
The Right ◽  
Linear Semidefinite Programming

This paper is devoted to the study of solving method for a type of inverse linear semidefinite programming problem in which both the objective parameter and the right-hand side parameter of the linear semidefinite programs are required to adjust. Since such kind of inverse problem is equivalent to a mathematical program with semidefinite cone complementarity constraints which is a rather difficult problem, we reformulate it as a nonconvex semi-definte programming problem by introducing a nonsmooth partial penalty function to penalize the complementarity constraint. The penalized problem is actually a nonsmooth DC programming problem which can be solved by a sequential convex program approach. Convergence analysis of the penalty models and the sequential convex program approach are shown. Numerical results are reported to demonstrate the efficiency of our approach.

AN UPPER BOUND FOR THE NUMBER OF DIFFERENT SOLUTIONS GENERATED BY THE PRIMAL SIMPLEX METHOD WITH ANY SELECTION RULE OF ENTERING VARIABLES

2013 ◽  
Vol 30 (03) ◽  
pp. 1340012 ◽  
Author(s):  
TOMONARI KITAHARA ◽  
SHINJI MIZUNO
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Upper Bound ◽  
Linear Programming Problem ◽  
Simplex Method ◽  
Selection Rule ◽  
Dual Simplex Method ◽  
Unimodular Matrix ◽  
Dual Simplex ◽  
Pivoting Rule

Recently, Kitahara, and Mizuno derived an upper bound for the number of different solutions generated by the primal simplex method with Dantzig's (the most negative) pivoting rule. In this paper, we obtain an upper bound with any pivoting rule which chooses an entering variable whose reduced cost is negative at each iteration. The upper bound is applied to a linear programming problem with a totally unimodular matrix. We also obtain a similar upper bound for the dual simplex method.

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