# Properties of Optimal Solution of Indefinite Matrix Constraint in Linear Programming

### Abstract

This study investigated characteristics of indefinite random square matrices which represented the constraints of Linear programming problems. MATLAB simulation was used to generate different size of indefinite random non-symmetric square matrices. Solutions of primal problem and dual problem were deliberated and discussed. Based on simulation results, duality gap found in some of the indefinite non-symmetric matrices and those matrices could not obtain optimal solution whereas some ID matrices that fulfill certain conditions could achieve optimal solution and no duality gap is found. An indefinite non-symmetric matrix with all positive off-diagonal entries and alternate signs of determinant of leading principal minors surely confirmed the existence of optimal solution in linear programming problems.

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