Linearly Constrained Optimization and Simplex Algorithm
This chapter recalls some theoretical results on linearly constrained optimization with convex objective function. In the case of a linear or quadratic objective, we show existence of an optimal solution whenever the value of the problem is finite, as well as existence of a basic solution in the linear case. Lagrangian duality theory is presented. In the linear case, existence of a strictly complementary solutions is obtained whenever the optimal value of the problem is finite. Finally, the simplex algorithm is introduced in the last part of the chapter.
KeywordsLagrange Multiplier Basic Point Dual Problem Linear Problem Simplex Method
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