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Methods for Linearly Constrained Problems

In: Nonlinear Optimization

Author

Listed:
  • H. A. Eiselt

    (University of New Brunswick)

  • Carl-Louis Sandblom

    (Dalhousie University)

Abstract

In this and the following two chapters, several algorithms for solving nonlinear constrained optimization problems will be described. First the most special of all constrained nonlinear programming problems is considered, namely the quadratic programming problem for which the objective function is convex and quadratic and the constraints are linear. In the second section of the chapter methods for the more general problem of optimizing a differentiable convex function subject to linear constraints are discussed. Although every convex quadratic programming problem could be solved also by these more general methods, it is generally preferable to employ quadratic programming methods when possible. As a general principle it is advisable to use more specialized techniques for more specialized problems. Consequently, for a given problem one should select a method (covered in the previous, this, or the next two chapters) from a box as high up in Table 6.1 as possible. The third section considers problems in which the objective function is quadratic, but concave, a difficult case.

Suggested Citation

  • H. A. Eiselt & Carl-Louis Sandblom, 2019. "Methods for Linearly Constrained Problems," International Series in Operations Research & Management Science, in: Nonlinear Optimization, chapter 0, pages 195-242, Springer.
    • Handle: RePEc:spr:isochp:978-3-030-19462-8_6
    DOI: 10.1007/978-3-030-19462-8_6
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