Expected utility, penalty functions, and duality in stochastic nonlinear programming

Article Abstract:

Duality theory related to stochastic nonlinear mathematical programming is researched, and a unified framework is presented for inferring duality results for stochastic mathematical programs. Established procedures in stochastic programming, including mean-variance analysis, reliability programming, stochastic goal programming, and chance constraints, are compared. An examination of programming penalty functions, duality, and expected utility in stochastic nonlinear programming focuses on the following areas: utility functions; concavity of certainty equivalence; properties of the U-penalty; exponential utility; a certainty equivalent and correlating penalty functions; duality results; and relations to other approaches to programming.

Models, Stochastic processes, Nonlinear programming

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Use of sample information in stochastic resource and chance-constrained programming models

Article Abstract:

Most probabilistic linear programming models assume the decision - maker knows the probability distributions for random model parameters. In this research, the decision - maker does not know such distributions, but has access to a random sample drawing. For two - stage stochastic programming with recourse models, the deterministic equivalent model is developed by using Bayesian methods. Chance - constrained programming models are also addressed.

Stochastic analysis, Structured programming

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Implicit treatment of 'zero or range' constraints in a model for minimum cost foundry alloys

Article Abstract:

Mixed-integer programming can be used to solve problems of producing a specified alloy at minimum cost from pure metals and scrap alloys. Computation times are reduced by a factor of three by implicitly treating 'zero or range' restraints for the selected amount of scrap alloy in the same way that bounds are treated in bounded variables linear programming.

Analysis, Linear programming, Founding, Casting (Metal)

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