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

Stein Lution 

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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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