Abstract
Robust optimization has come out to be a potent approach to study mathematical problems with data uncertainty. We use robust optimization to study a nonsmooth nonconvex mathematical program over cones with data uncertainty containing generalized convex functions. We study sufficient optimality conditions for the problem. Then we construct its robust dual problem and provide appropriate duality theorems which show the relation between uncertainty problems and their corresponding robust dual problems.
Highlights
Data uncertainty may be due to various factors, like measurement/prediction errors or unknown future demands
Robust Optimization (RO) technique is applied for handling such scenarios as it considers all the possible data perturbations into one big picture and gives an immunized solution
This paper deals with two main components of mathematical programs structured from the real world problems: one is the uncertainty in the data infused to the model and the other is nonsmooth non-convex functions being a part of the mathematical model
Summary
Data uncertainty may be due to various factors, like measurement/prediction errors or unknown future demands. Robust Optimization (RO) technique is applied for handling such scenarios as it considers all the possible data perturbations into one big picture and gives an immunized solution This deterministic approach works well even for the worst possible case of uncertainty. This paper deals with two main components of mathematical programs structured from the real world problems: one is the uncertainty in the data infused to the model and the other is nonsmooth non-convex functions being a part of the mathematical model. While the former is quite young as a research field, the latter has its root dating back to 1949.
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