article · Mathematics of Operations Research · 1995

Nonlinear Extensions of Farkas’ Lemma with Applications to Global Optimization and Least Squares

Cited by 25Abstract and details only

Abstract

A nonlinear extension of Farkas’ lemma for systems involving the difference of sublinear functions is presented. This extension of Farkas’ lemma is applied to give a complete characterization of global optimality for constrained global optimization problems in which the objective function is the difference of a convex and sublinear function and the constraints are systems of difference sublinear functions. An application to certain fractional programming problems is also given. These results are achieved with merely a stronger consistency condition which reduces to the usual feasibility requirement for problems with sublinear constraints. Further generalizations of Farkas’ lemma for systems involving convex and difference sublinear functions are also presented. Moreover, a generalized Farkas’ lemma for certain specially structural convex inequality systems is shown to be related to the solution of appropriate constrained least squares problems.

Cite this paper

APA 7

Jeyakumar, V., & Glover, B. M. (1995). Nonlinear Extensions of Farkas’ Lemma with Applications to Global Optimization and Least Squares. Mathematics of Operations Research, 20(4), 818–837. https://doi.org/10.1287/moor.20.4.818

MLA 9

Jeyakumar, V., and B. M. Glover. “Nonlinear Extensions of Farkas’ Lemma with Applications to Global Optimization and Least Squares.” Mathematics of Operations Research, vol. 20, no. 4, 1995, pp. 818–37, https://doi.org/10.1287/moor.20.4.818.

Chicago

Jeyakumar, V., and B. M. Glover. 1995. “Nonlinear Extensions of Farkas’ Lemma with Applications to Global Optimization and Least Squares.” Mathematics of Operations Research 20 (4): 818–37. https://doi.org/10.1287/moor.20.4.818.

Harvard

Jeyakumar, V. and Glover, B.M. (1995) ‘Nonlinear Extensions of Farkas’ Lemma with Applications to Global Optimization and Least Squares’, Mathematics of Operations Research, 20(4), pp. 818–837. Available at: https://doi.org/10.1287/moor.20.4.818.

BibTeX

@article{jeyakumar1995nonlinear,
  title = {{Nonlinear Extensions of Farkas’ Lemma with Applications to Global Optimization and Least Squares}},
  author = {Jeyakumar, V. and Glover, B. M.},
  journal = {Mathematics of Operations Research},
  volume = {20},
  number = {4},
  pages = {818--837},
  year = {1995},
  doi = {10.1287/moor.20.4.818}
}

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