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INTRODUCTION TO LINEAR PROGRAMMING l
DUAL LINEAR PROGRAMS
ELEMENTS OF THE THEORY OF LINEAR SYSTEMS
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augmented matrix basic solution associated basic solution corresponding basic variables basis is optimal canonical form Chapter column complementary slackness theorem Consider the linear convex function convex program convex set corresponding basic solution defined Definition denote domain of feasible dual feasible dual linear programs dual simplex algorithm dual variables elementary row operations enter the basis equivalent example Exercise feasible basis feasible solution finite form with respect full rank half space hyperplane linear program CP linear system m-column vector m-matrix matrix of coefficients mxn-matrix n-row vector nonbasic variables nonzero elements objective function optimal basis optimal solution pivot operation polynomial primal Proof prove raw material redundant equation Remark l2 resp revised simplex algorithm Section set of feasible Show simplex method slack variables Solve the linear standard form Step Theorem IV.3 transportation problem triangular triangular matrix unit matrix vertex written in canonical z(Max z(Min zero