Monotone Approximation of Decision Problems

Authors:
Naveed Chehrazi;Thomas A. Weber
Affiliations:
Department of Management Science and Engineering, Stanford University, Stanford, California 94305;Department of Management Science and Engineering, Stanford University, Stanford, California 94305
Venue:
Operations Research
Year:
2010

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Abstract

Many decision problems exhibit structural properties in the sense that the objective function is a composition of different component functions that can be identified using empirical data. We consider the approximation of such objective functions, subject to general monotonicity constraints on the component functions. Using a constrained B-spline approximation, we provide a data-driven robust optimization method for environments that can be sample-sparse. The method, which simultaneously identifies and solves the decision problem, is illustrated for the problem of optimal debt settlement in the credit-card industry.