# Robust Discrete Optimization And Its Applications Pdf

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## Robust optimization

Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. A Frank-Wolfe Based Algorithm for Robust Discrete Optimization under Uncertainty Abstract: This paper addresses a class of robust optimization problems whose inputs are correlated and belong to an ellipsoidal uncertainty set, which is known to be NP-Hard.

For that, we propose an efficient heuristic scalable approach based on the iterative Frank-Wolfe FW algorithm. In our approach, we take a radically different perspective on FW by looking at the exploration power of the integer inner iterates of the method.

Our main discovery is that, for small dimensional instances, our method is able to provide the same optimal integer solution as an exact method provided by CPLEX, after no more than a few hundred iterations.

Moreover, as opposed to the exact method, our FW-guided integer exploration approach applies to large scale problems as well. Our findings are illustrated by comprehensive numerical experiments. We focus on two target applications, the robust shortest path problem as a first test case, and the robust clustering as a real application in a PHM context and data analysis. Article :. DOI: Need Help?

## Types of Optimization Problems

As noted in the Introduction to Optimization , an important step in the optimization process is classifying your optimization model, since algorithms for solving optimization problems are tailored to a particular type of problem. Here we provide some guidance to help you classify your optimization model; for the various optimization problem types, we provide a linked page with some basic information, links to algorithms and software, and online and print resources. For an alphabetical listing of all of the linked pages, see Optimization Problem Types: Alphabetical Listing. While it is difficult to provide a taxonomy of optimization, see Optimization Taxonomy for one perspective. Skip to main content.

Semidefinite programming refers to the problem of minimizing a linear objective subject to semidefiniteness constraints involving symmetric matrices that are affine in the decision variables. Such a model of computation has enjoyed tremendous interest recently, due to its ubiquity in many areas of science and engineering. This workshop will cover theory and algorithms of SDP and several application areas, including but not limited to:. Students, recent Ph. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available. MSRI does not hire an outside company to make hotel reservations for our workshop participants, or share the names and email addresses of our participants with an outside party.

Ben-tal and A. Nemirovski , Robust solutions of Linear Programming problems contaminated with uncertain data , Mathematical Programming , vol. DOI : Bertsimas and M. Poss , Robust combinatorial optimization with variable budgeted uncertainty , 4OR , vol. Aissi, C.

Robust Discrete Optimization and Its Applications. Authors; (view PDF · A Robust Discrete Optimization Framework. Panos Kouvelis, Gang Yu. Pages

## Robust discrete optimization and network flows

The origins of robust optimization date back to the establishment of modern decision theory in the s and the use of worst case analysis and Wald's maximin model as a tool for the treatment of severe uncertainty. It became a discipline of its own in the s with parallel developments in several scientific and technological fields. Over the years, it has been applied in statistics , but also in operations research , [1] electrical engineering , [2] [3] control theory , [4] finance , [5] portfolio management [6] logistics , [7] manufacturing engineering , [8] chemical engineering , [9] medicine , [10] and computer science. Consider the following linear programming problem.

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