A bilevel bottleneck programming problem

Article Abstract:

A non-convex programming problem with linear constraints and which require the minimization of concave bottleneck functions at two levels is considered. Such bilevel programming problems are encountered in organizations where decision makers exist at two hierarchical levels. To obtain a global optimal solution, the extreme point search procedure is employed. It entails the derivation of 'an extreme point of the underlying region' and the ranking of the outer level objective function values.

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Ranking in quadratic integer programming problems

Article Abstract:

A procedure for ranking the set of integer feasible solutions to a quadratic integer programming (QIP) problem in increasing order of the objective function values is introduced. The procedure involves the formulation of a related linear integer programming problem to derive bounds on the objective function of the QIP. Consequently, it derives the optimal integer feasible solution to QIP problems subject to nonlinear constraints.

Operations research, Management science, Case studies, Quadratic programming

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A nonlinear programming model for partially observable Markov decision processes: finite horizon case

Article Abstract:

An alternative approach for addressing the lack of data 'about the state of a Markov decision processes' is introduced. The technique, which is computationally less complex than methods based on Markov process theory, involves reformulating the problem in a nonlinear programming framework. This facilitates its solution using a policy iteration procedure based on the method of feasible direction.

Markov processes

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