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Linearly Constrained Optimization and Simplex Algorithm

  • J. Frédéric Bonnans
  • J. Charles Gilbert
  • Claude Lemaréchal
  • Claudia A. Sagastizábal
Part of the Universitext book series (UTX)

Overview

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.

Keywords

Lagrange Multiplier Basic Point Dual Problem Linear Problem Simplex Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • J. Frédéric Bonnans
    • 1
  • J. Charles Gilbert
    • 1
  • Claude Lemaréchal
    • 2
  • Claudia A. Sagastizábal
    • 3
  1. 1.INRIA RocquencourtLe ChesnayFrance
  2. 2.INRIA Rhône-AlpesMontbonnot, Saint IsmierFrance
  3. 3.IMPAJardim Botânico, Rio de Janeiro-RJBrazil

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