196 results found
Giacometti R, Rustem B, 2019, 14th International Conference on Computational Management Science, COMPUTATIONAL MANAGEMENT SCIENCE, Vol: 16, Pages: 1-2, ISSN: 1619-697X
Kapsos M, Christofides N, Rustem B, 2018, Robust risk budgeting, ANNALS OF OPERATIONS RESEARCH, Vol: 266, Pages: 199-221, ISSN: 0254-5330
Parpas P, Rustem, Duy VN Luong, et al., 2016, A weighted Mirror Descent algorithm for nonsmooth convex optimization problem, Journal of Optimization Theory and Applications, Vol: 170, Pages: 900-915, ISSN: 1573-2878
Large scale nonsmooth convex optimization is a common problemfor a range of computational areas including machine learning and computer vision. Problems in these areas contain special domain structures and characteristics. Special treatment of such problem domains, exploiting their structures, can significantly reduce the computational burden. In this paper, we consider a Mirror Descent method with a special choice of distance function for solving nonsmooth optimization problems over a Cartesian product of convex sets. We propose to use a nonlinear weighted distance in the projectionstep. The convergence analysis identifies optimal weighting parameters that, eventually, lead to the optimally weighted step-size strategy for every projection on a corresponding convex set. We show that the optimality bound of the Mirror Descent algorithm using the weighted distance is either an improvement to, or in the worst-case as good as, the optimality bound of the Mirror Descent using unweighted distances. We demonstrate the efficiency of the algorithm by solving the Markov Random Fields (MRF) optimization problem. In order to exploit the domain of the MRF problem, we use a weighted logentropy distance and a weighted Euclidean distance. Promising experimentalresults demonstrate the effectiveness of the proposed method.
Faísca NP, Rustem B, Dua V, 2014, Bilevel and Multilevel Programming, Process Systems Engineering, Pages: 129-149, ISBN: 9783527316847
Kuhn D, Parpas P, Rustem B, 2014, Stochastic Optimization of Investment Planning Problems in the Electric Power Industry, Process Systems Engineering, Pages: 215-230, ISBN: 9783527316847
© 2014 Wiley-VCH Verlag GmbH & Co. KGaA. All rights reserved. Decisions on whether to invest in new power system infrastructure can have farreaching consequences. The timely expansion of generation and transmission capacities is crucial for the reliability of a power system and its ability to provide uninterrupted service under changing market conditions.We consider a local (e.g., regional or national) power system which is embedded into a deregulated electricity market. Assuming a probabilistic model for future electricity demand, fuel prices, equipment failures, and electricity spot prices, we formulate a capacity expansion problem which minimizes the sum of the costs for upgrading the local power system and the costs for operating the upgraded system over an extended planning horizon. The arising optimization problem represents a two-stage stochastic program with binary first-stage decisions. Solution of this problem relies on a specialized algorithm which constitutes a symbiosis of a regularized decomposition method and a branch-and-bound scheme.
Kakouris I, Rustem B, 2014, Robust portfolio optimization with copulas, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, Vol: 235, Pages: 28-37, ISSN: 0377-2217
Kapsos M, Christofides N, Rustem B, 2014, Worst-case robust Omega ratio, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, Vol: 234, Pages: 499-507, ISSN: 0377-2217
Kapsos M, Zymler S, Christofides N, et al., 2014, Optimizing the Omega ratio using linear programming, JOURNAL OF COMPUTATIONAL FINANCE, Vol: 17, Pages: 49-57, ISSN: 1460-1559
Kong FW, Rustem B, 2013, Welfare-maximizing correlated equilibria using Kantorovich polynomials with sparsity, JOURNAL OF GLOBAL OPTIMIZATION, Vol: 57, Pages: 251-277, ISSN: 0925-5001
Kong FW, Parpas P, Rustem B, 2013, Sum of Non-Concave Utilities Maximization for MIMO Interference Systems, IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, Vol: 12, Pages: 1744-1751, ISSN: 1536-1276
We study a variant of the pessimistic bi-level optimization problem, which comprisesconstraints that must be satisfied for any optimal solution of a subordinate (lower-level) optimization problem. We present conditions that guarantee the existence of optimal solutions in such a problem, and we characterize the computational complexity of various subclasses of the problem. We then focus on problem instances that may lack convexity, but that satisfy a certain independence property. We develop convergent approximations for these instances, and we derive an iterative solution scheme that is reminiscent of the discretization techniques used in semi-infinite programming. We also present a computational study that illustrates the numerical behavior of our algorithm on standard benchmark instances.
Fonseca RJ, Rustem B, 2012, International portfolio management with affine policies, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, Vol: 223, Pages: 177-187, ISSN: 0377-2217
Zymler S, Kuhn D, Rustem B, 2012, Distributionally Robust Joint Chance Constraints with Second-Order Moment Information, Mathematical Programming, ISSN: 0025-5610
We develop tractable semidefinite programming based approximations for distributionally robust individual and joint chance constraints, assuming that only the first- and second-order moments as well as the support of the uncertain parameters are given. It is known that robust chance constraints can be conservatively approximated by Worst-Case Conditional Value-at-Risk (CVaR) constraints. We first prove that this approximation is exact for robust individual chance constraints with concave or (not necessarily concave) quadratic constraint functions, and we demonstrate that the Worst-Case CVaR can be computed efficiently for these classes of constraint functions. Next, we study the Worst-Case CVaR approximation for joint chance constraints. This approximation affords intuitive dual interpretations and is provably tighter than two popular benchmark approximations. The tightness depends on a set of scaling parameters, which can be tuned via a sequential convex optimization algorithm. We show that the approximation becomes essentially exact when the scaling parameters are chosen optimally and that the Worst-Case CVaR can be evaluated efficiently if the scaling parameters are kept constant.We evaluate our joint chance constraint approximation in the context of a dynamic water reservoir control problem and numerically demonstrate its superiority over the two benchmark approximations.
Fonseca RJ, Rustem B, 2012, Robust hedging strategies, COMPUTERS & OPERATIONS RESEARCH, Vol: 39, Pages: 2528-2536, ISSN: 0305-0548
Wiesemann W, Kuhn D, Rustem B, 2012, Robust Markov Decision Processes, Mathematics of Operations Research, ISSN: 1526-5471
Markov decision processes (MDPs) are powerful tools for decision making in uncertain dynamic environments. However, the solutions of MDPs are of limited practical use because of their sensitivity to distributional model parameters, which are typically unknown and have to be estimated by the decision maker. To counter the detrimental effects of estimation errors, we consider robust MDPs that offer probabilistic guarantees in view of the unknown parameters. To this end, we assume that an observation history of the MDP is available. Based on this history, we derive a confidence region that contains the unknown parameters with a prespecified probability 1-β. Afterward, we determine a policy that attains the highest worst-case performance over this confidence region. By construction, this policy achieves or exceeds its worst-case performance with a confidence of at least 1-β. Our method involves the solution of tractable conic programs of moderate size.
Wiesemann W, Kuhn D, Rustem B, 2012, Robust Resource Allocations in Temporal Networks, Mathematical Programming, Vol: 135, Pages: 437-471
Temporal networks describe workflows of time-consuming tasks whose processing order is constrained by precedence relations. In many cases, the durations of the network tasks can be influenced by the assignment of resources. This leads to the problem of selecting an ‘optimal’ resource allocation, where optimality is measured by network characteristics such as the makespan (i.e., the time required to complete all tasks). In this paper we study a robust resource allocation problem where the task durations are uncertain, and the goal is to minimise the worst-case makespan. We show that this problem is generically -hard. We then develop convergent bounds on the optimal objective value, as well as feasible allocations whose objective values are bracketed by these bounds. Numerical results provide empirical support for the proposed method.
Kong FW, Kleniati P-M, Rustem B, 2012, Computation of Correlated Equilibrium with Global-Optimal Expected Social Welfare, JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, Vol: 153, Pages: 237-261, ISSN: 0022-3239
Vayanos P, Kuhn D, Rustem B, 2012, A constraint sampling approach for multi-stage robust optimization, AUTOMATICA, Vol: 48, Pages: 459-471, ISSN: 0005-1098
Wiesemann W, Kuhn D, Rustem B, 2012, Multi-resource allocation in stochastic project scheduling, ANNALS OF OPERATIONS RESEARCH, Vol: 193, Pages: 193-220, ISSN: 0254-5330
Fonseca RJ, Wiesemann W, Rustem B, 2012, Robust international portfolio management, Computational Management Science, Vol: 9, Pages: 31-62, ISSN: 1619-697X
We present an international portfolio optimization model where we take into account the two different sources of return of an international asset: the local returns denominated in the local currency, and the returns on the foreign exchange rates. The explicit consideration of the returns on exchange rates introduces non-linearities in the model, both in the objective function (return maximization) and in the triangulation requirement of the foreign exchange rates. The uncertainty associated with both types of returns is incorporated directly in the model by the use of robust optimization techniques. We show that, by using appropriate assumptions regarding the formulation of the uncertainty sets, the proposed model has a semidefinite programming formulation and can be solved efficiently. While robust optimization provides a guaranteed minimum return inside the uncertainty set considered, we also discuss an extension of our formulation with additional guarantees through trading in quanto options for the foreign assets and in equity options for the domestic assets. © 2011 Springer-Verlag.
Luong DVN, Parpas P, Rueckert D, et al., 2012, Solving MRF Minimization by Mirror Descent, 8th International Symposium on Visual Computing (ISVC), Publisher: SPRINGER-VERLAG BERLIN, Pages: 587-598, ISSN: 0302-9743
Zymler S, Kuhn D, Rustem B, 2012, Worst-Case Value-at-Risk of Non-Linear Portfolios, Management Science, ISSN: 0025-1909
Portfolio optimization problems involving value at risk (VaR) are often computationally intractable and require complete information about the return distribution of the portfolio constituents, which is rarely available in practice. These difficulties are compounded when the portfolio contains derivatives. We develop two tractable conservative approximations for the VaR of a derivative portfolio by evaluating the worst-case VaR over all return distributions of the derivative underliers with given first- and second-order moments. The derivative returns are modelled as convex piecewise linear or—by using a delta–gamma approximation—as (possibly nonconvex) quadratic functions of the returns of the derivative underliers. These models lead to new worst-case polyhedral VaR (WPVaR) and worst-case quadratic VaR (WQVaR) approximations, respectively. WPVaR serves as a VaR approximation for portfolios containing long positions in European options expiring at the end of the investment horizon, whereas WQVaR is suitable for portfolios containing long and/or short positions in European and/or exotic options expiring beyond the investment horizon. We prove that—unlike VaR that may discourage diversification—WPVaR and WQVaR are in fact coherent risk measures. We also reveal connections to robust portfolio optimization.
Tsoukalas A, Rustem B, 2011, A feasible point adaptation of the Blankenship and Falk algorithm for semi-infinite programming, OPTIMIZATION LETTERS, Vol: 5, Pages: 705-716, ISSN: 1862-4472
Fonseca RJ, Zymler S, Wiesemann W, et al., 2011, Robust optimization of currency portfolios, JOURNAL OF COMPUTATIONAL FINANCE, Vol: 15, Pages: 3-30, ISSN: 1460-1559
Kuhn D, Parpas P, Rustem B, 2011, Stochastic Optimization of Investment Planning Problems in the Electric Power Industry, Vol: 5, Pages: 215-230
Decisions on whether to invest in new power system infrastructure can have farreaching consequences. The timely expansion of generation and transmission capacities is crucial for the reliability of a power system and its ability to provide uninterrupted service under changing market conditions.We consider a local (e.g., regional or national) power system which is embedded into a deregulated electricity market. Assuming a probabilistic model for future electricity demand, fuel prices, equipment failures, and electricity spot prices, we formulate a capacity expansion problem which minimizes the sum of the costs for upgrading the local power system and the costs for operating the upgraded system over an extended planning horizon. The arising optimization problem represents a two-stage stochastic program with binary first-stage decisions. Solution of this problem relies on a specialized algorithm which constitutes a symbiosis of a regularized decomposition method and a branch-and-bound scheme. © 2008 Wiley-VCH Verlag GmbH & Co. KGaA.
Ye K, Parpas P, Rustem B, Robust portfolio optimization: a conic programming approach, Computational Optimization and Applications, Pages: 1-19-1-19, ISSN: 0926-6003
Faísca NP, Rustem B, Dua V, 2011, Bilevel and Multilevel Programming, Vol: 1, Pages: 129-149
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