Bram L. Gorissen

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This paper addresses the robust counterparts of optimization problems containing sums of maxima of linear functions. These problems include many practical problems, e.g. problems with sums of absolute values, and arise when taking the robust counterpart of a linear inequality that is affine in the decision variables, affine in a parameter with box(More)
We propose a new way to derive tractable robust counterparts of a linear program by using the theory of Beck and Ben-Tal (2009) on the duality between the robust (" pessimistic ") primal problem and its " optimistic " dual. First, we obtain a new convex reformulation of the dual problem of a robust linear program, and then show how to construct the primal(More)
We propose a new way to derive tractable robust counterparts of a linear program by using the theory of Beck and Ben-Tal (2009) on the duality between the robust (" pessimistic ") primal problem and its " optimistic " dual. First, we obtain a new convex reformulation of the dual problem of a robust linear program, and then show how to construct the primal(More)
Robust optimization is a young and active research field that has been mainly developed in the last 15 years. Robust optimization is very useful for practice, since it is tailored to the information at hand, and it leads to computationally tractable formulations. It is therefore remarkable that real-life applications of robust optimization are still lagging(More)
The dual problem of a convex optimization problem can be obtained in a relatively simple and structural way by using a well-known result in convex analysis, namely Fenchel's duality theorem. This alternative way of forming a strong dual problem is the subject in this paper. We recall some standard results from convex analysis and then discuss how the dual(More)
Current inverse treatment planning methods that optimize both catheter positions and dwell times in prostate HDR brachytherapy use surrogate linear or quadratic objective functions that have no direct interpretation in terms of dose-volume histogram (DVH) criteria, do not result in an optimum or have long solution times. We decrease the solution time of the(More)
Inverse planning algorithms for dwell time optimisation in interstitial high-dose-rate (HDR) brachytherapy may produce solutions with large dwell time variations within catheters, which may result in undesirable selective high-dose subvolumes. Extending the dwell time optimisation model with a dwell time modulation restriction (DTMR) that limits dwell time(More)