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Convex Programming

  • Robert J. Vanderbei
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 196)

Abstract

In the last chapter, we saw that small modifications to the primal–dual interior-point algorithm allow it to be applied to quadratic programming problems as long as the quadratic objective function is convex. In this chapter, we shall go further and allow the objective function to be a general (smooth) convex function. In addition, we shall allow the feasible region to be any convex set given by a finite collection of convex inequalities.

Bibliography

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  2. Fiacco, A., and McCormick, G. (1968). Nonlinear programming: Sequential unconstrained minimization techniques. McLean: Research Analysis Corporation. Republished in 1990 by SIAM, Philadelphia.Google Scholar
  3. Nesterov, Y., and Nemirovsky, A. (1993). Interior point polynomial methods in convex programming: Theory and algorithms. Philadelphia: SIAM.Google Scholar
  4. Vanderbei, R., and Shanno, D. (1999). http://www.sor.princeton.edu/~rvdb/ps/nonlin.pdfAn interior-point algorithm for nonconvex nonlinear programming. Computational Optimization and Applications, 13, 231–252.

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Robert J. Vanderbei
    • 1
  1. 1.Department of Operations Research and Financial EngineeringPrinceton UniversityPrincetonUSA

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