We describe software for stochastic programming that uses only sampled data to obtain both a consistent sample-average solution and a consistent estimate of confidence intervals for the optimality gap using bootstrap and bagging. The underlying distribution whence the samples come is not required. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0253 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0253 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

The “From the Editor” laments the passing of Saul Gass and Arne Løkketangen, and describes the journal's new data policy.

We describe computational procedures for solving a wide-ranging class of stochastic programs with chance constraints where the random components of the problem are discretely distributed. Our procedures are based on a combination of Lagrangian relaxation and scenario decomposition, which we solve using a novel variant of Rockafellar and Wets' progressive hedging algorithm [Rockafellar, R. T., R. J.-B. Wets. 1991. Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res. 16(1) 119–147]. Experiments demonstrate the ability of the proposed algorithm to quickly find near-optimal solutions—where verifiable—to both difficult and very large chance-constrained stochastic programs, both with and without integer decision variables. The algorithm exhibits strong scalability in terms of both run time required and final solution quality on large-scale instances. There is a Video Overview associated with this paper. Click here to view the Video Overview . To save the file, right click and choose “Save Link As” from the menu.

In this paper we describe a ghost image processing (see Glover [Glover, F. 1994. Optimization by Ghost image processing in neural networks. Comput. Oper. Res. 21(8) 801–822.] application to the problem of finding the minimum covariance determinant (MCD) estimator of multi-variate shape and location (see Rousseeuw [Rousseeuw, P. J. 1985. Multivariate estimation with high breakdown point. W. Grossman, G. Pflug, I. Vincze, W. Werz, eds. Mathematical Statistics and Applications, Vol. B. Dordrecht, Reidel.]). The MCD is resistant to contamination and has other desirable statistical properties but is difficult to compute. Ghost image processing offers an opportunity to make use of knowledge of the form of solutions when constructing algorithms to solve hard combinatorial optimization problems. Experimental results and comparisons with steepest descent lend additional insights. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.