On Optimality Functions in Stochastic Programming and Applications
MetadataShow full item record
Optimality functions define stationarity in nonlinear programming, semi-infinite optimization, and optimal control in some sense. In this paper, we consider optimality functions for stochastic programs with nonlinear, possibly nonconvex, expected value objective and constraint functions. We show that an optimality function directly relates to the difference in function values at a candidate point and a local minimizer. We construct confidence intervals for the value of the optimality function at a candidate point and, hence, provide a quantitative measure of solution quality. Based on sample average approximations, we develop two algorithms for classes of stochastic programs that include CVaR-problems and utilize optimality functions to select sample sizes as well as “active” sample points in an active-set strategy. Numerical tests illustrate the procedures.
Showing items related by title, author, creator and subject.
Cormican, Kelly James (Monterey, California. Naval Postgraduate School, 1995-03);Using limited resources, a network interdictor attempts to disable components of a capacitated network with the objective of minimizing the maximum network flow achievable by the network user. This problem has applications ...
Phelps, Chris; Gong, Qi; Royset, Johannes O.; Walton, Claire; Kaminer, Isaac (Elsevier, 2014);This paper focuses on a non-standard constrained nonlinear optimal control problem in which the objective functional involves an integration over a space of stochastic parameters as well as an integration over the time ...
Feuer, Arie; Cristi, Roberto (IEEE, 1993-06);In this correspondence we investigate the solution to the following problem: Find the optimal weighted sum of given signals when the optimality criteria is the expected value of a function of this sum and a given "training" ...