A sequential algorithm for solving nonlinear optimization problems with chance constraints

Frank E. Curtis, Andreas Wächter, Victor M. Zavala

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


An algorithm is presented for solving nonlinear optimization problems with chance constraints, i.e., those in which a constraint involving an uncertain parameter must be satisfied with at least a minimum probability. In particular, the algorithm is designed to solve cardinality-constrained nonlinear optimization problems that arise in sample average approximations of chance-constrained problems, as well as in other applications in which it is only desired to enforce a minimum number of constraints. The algorithm employs a novel exact penalty function which is minimized sequentially by solving quadratic optimization subproblems with linear cardinality constraints. Properties of minimizers of the penalty function in relation to minimizers of the corresponding nonlinear optimization problem are presented, and convergence of the proposed algorithm to stationarity with respect to the penalty function is proved. The effectiveness of the algorithm is demonstrated through numerical experiments with a nonlinear cash flow problem.

Original languageEnglish (US)
Pages (from-to)930-958
Number of pages29
JournalSIAM Journal on Optimization
Issue number1
StatePublished - 2018


  • Cardinality constraints
  • Chance constraints
  • Exact penalization
  • Nonlinear optimization
  • Sample average approximation
  • Sequential quadratic optimization
  • Trust region methods

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science


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