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Mustafa Ç. Pınar

Bio: Mustafa Ç. Pınar is an academic researcher from Bilkent University. The author has contributed to research in topics: Robust optimization & Portfolio. The author has an hindex of 20, co-authored 117 publications receiving 1617 citations. Previous affiliations of Mustafa Ç. Pınar include Université libre de Bruxelles & Technical University of Denmark.


Papers
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Journal ArticleDOI
TL;DR: The robust spanning tree problem is defined to hedge against the worst case contingency, some useful optimality concepts are defined, and characterizations for these entities leading to polynomial time recognition algorithms are presented.

173 citations

Journal ArticleDOI
TL;DR: The smoothing approximation is used as the basis of an algorithm for solving problems with embedded network structures, and nonlinear minimax problems, demonstrating the efficiency of this approach.
Abstract: A quadratic smoothing approximation to nondifferentiable exact penalty functions for convex constrained optimization is proposed and its properties are established The smoothing approximation is used as the basis of an algorithm for solving problems with (i) embedded network structures, and (ii) nonlinear minimax problems Extensive numerical results with large-scale problems illustrate the efficiency of this approach

112 citations

Journal ArticleDOI
TL;DR: A concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis and the approximate S-Lemma as well as its applications in robust optimization.
Abstract: We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization.

111 citations

Journal IssueDOI
01 Jan 2007-Networks
TL;DR: This work investigates a network design problem under traffic uncertainty that arises when provisioning Virtual Private Networks (VPNs), and presents compact linear mixed-integer programming formulations for the problem with the classical hose traffic model and for a less conservative robust variant relying on the traffic statistics that are often available.
Abstract: We investigate a network design problem under traffic uncertainty that arises when provisioning Virtual Private Networks (VPNs): given a set of terminals that must communicate with one another, and a set of possible traffic matrices, sufficient capacity has to be reserved on the links of the large underlying public network to support all possible traffic matrices while minimizing the total reservation cost. The problem admits several versions depending on the desired topology of the reserved links, and the nature of the traffic data uncertainty. We present compact linear mixed-integer programming formulations for the problem with the classical hose traffic model and for a less conservative robust variant relying on the traffic statistics that are often available. These flow-based formulations allow us to solve optimally medium-to-large instances with commercial MIP solvers. We also propose a combined branch-and-price and cutting-plane algorithm to tackle larger instances. Computational results obtained for several classes of instances are reported and discussed. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 49(1), 100–115 2007

84 citations

01 Jan 2012
TL;DR: It is shown that knowing those arcs which are never on shortest paths the authors can preprocess a graph prior to solution of the robust path problems, supporting the claim that the preprocessing of graphs helps us significantly in solving the robust paths problems.
Abstract: We investigate the well-known shortest path problem on directed acyclic graphs under arc length uncertainties. We model data uncertainty by treating the arc lengths as interval ranges. In order to handle uncertainty in the decision making process, a robustness approach is adopted. The robustness criteria used in the paper are the minimax (absolute robustness) criterion, and the minimax regret (robust deviation) criterion. Under these criteria, we define and identify paths which perform satisfactorily under any likely input data and give a mixed integer programming formulation to find them. We classify arcs based on the realization of the input data. We show that knowing those arcs which are never on shortest paths we can preprocess a graph prior to solution of the robust path problems. Computational results support our claim that the preprocessing of graphs helps us significantly in solving the robust path problems.

84 citations


Cited by
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Book
01 Jan 2013
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
Abstract: Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

1,957 citations

Journal ArticleDOI
TL;DR: This paper surveys the primary research, both theoretical and applied, in the area of robust optimization (RO), focusing on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology.
Abstract: In this paper we survey the primary research, both theoretical and applied, in the area of robust optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying prominent theoretical results of RO, we also present some recent results linking RO to adaptable models for multistage decision-making problems. Finally, we highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.

1,863 citations

Journal ArticleDOI
TL;DR: This paper characterize the desirable properties of a solution to models, when the problem data are described by a set of scenarios for their value, instead of using point estimates, and develops a general model formulation, called robust optimization RO, that explicitly incorporates the conflicting objectives of solution and model robustness.
Abstract: Mathematical programming models with noisy, erroneous, or incomplete data are common in operations research applications. Difficulties with such data are typically dealt with reactively-through sensitivity analysis-or proactively-through stochastic programming formulations. In this paper, we characterize the desirable properties of a solution to models, when the problem data are described by a set of scenarios for their value, instead of using point estimates. A solution to an optimization model is defined as: solution robust if it remains "close" to optimal for all scenarios of the input data, and model robust if it remains "almost" feasible for all data scenarios. We then develop a general model formulation, called robust optimization RO, that explicitly incorporates the conflicting objectives of solution and model robustness. Robust optimization is compared with the traditional approaches of sensitivity analysis and stochastic linear programming. The classical diet problem illustrates the issues. Robust optimization models are then developed for several real-world applications: power capacity expansion; matrix balancing and image reconstruction; air-force airline scheduling; scenario immunization for financial planning; and minimum weight structural design. We also comment on the suitability of parallel and distributed computer architectures for the solution of robust optimization models.

1,793 citations

Journal Article
TL;DR: In this article, the authors survey the primary research, both theoretical and applied, in the area of robust optimization and highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.
Abstract: In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying prominent theoretical results of RO, we also present some recent results linking RO to adaptable models for multi-stage decision-making problems. Finally, we highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.

1,633 citations