## Introduction to methods of optimization |

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artificial variables assume basic feasible solution boundary point branch and bound calculate Chapter column components computational concave function constraints convex combination convex function convex hull convex polyhedron convex set defined definition derivatives determine discussed dynamic programming elements enter the basis equation example extreme points finite number flow formulation function f(x functional evaluations gi(x given global maximum gradient Hence inequalities integer programming integer solution interval of uncertainty iteration line segment linear programming problem linearly independent Maximize minimize minimum multiplying node nonlinear programming nonnegative number of variables objective function obtain off(x optimal solution optimization problem original problem points xu x2 positive possible primal procedure relative maximum result satisfied scalar search methods shown in Figure simplex algorithm simplex method solve stationary point supporting hyperplane Suppose Table tableau Theorem transportation problem unimodal upper bound wish yields zero