A Constant Rank Constraint Qualification in Continuous-Time Nonlinear Programming

Abstract

The paper addresses continuous-time nonlinear programming problems with equality and inequality constraints. First and second order necessary optimality conditions are obtained under a constant rank type constraint qualification. The first order necessary conditions are of Karush-Kuhn-Tucker type.

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Acknowledgements

The authors are grateful to Professor Roberto Andreani for pointing out the paper Andreani et al. [4], specifically Lemmas 1 and 2, and for fruitful discussions on constraint qualifications.

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Correspondence to Valeriano Antunes de Oliveira.

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V.A. de Oliveira was partially supported by grants 2013/07375-0 and 2016/03540-4 from the São Paulo Research Foundation (FAPESP), and by grants 457785/2014-4 and 310955/2015-7, from the National Council for Scientific and Technological Development (CNPq).

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do Monte, M.R.C., de Oliveira, V.A. A Constant Rank Constraint Qualification in Continuous-Time Nonlinear Programming. Set-Valued Var. Anal 29, 61–81 (2021). https://doi.org/10.1007/s11228-020-00537-1

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Keywords

  • Nonlinear programming
  • Continuous-time programming
  • Necessary optimality conditions
  • Constraint qualifications
  • Constant rank condition

Mathematics Subject Classification (2010)

  • 90C30
  • 90C46