Cutting-set methods for robust convex optimization with pessimizing oracles

Mutapcic, Almir; Boyd, Stephen

doi:10.1080/10556780802712889

Cited by 122 publications

(171 citation statements)

References 91 publications

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“…This algorithm employs an iterative procedure, known as the cutting-set method [32], which switches between two steps in each iteration: optimization and pessimization (worst-case analysis). In the optimization step, a sampled version of the semi-infinite problem is solved over finite subsets of the uncertainty regions.…”

Section: Cutting-set Methodsmentioning

confidence: 99%

“…The cutting-set algorithm converges to the optimum solution of the original problem given that the optimization and pessimization steps are solved to global optimality in each iteration [32]. However, the optimization step here involves solving the non-convex problem in (25), and hence global optimality may not be guaranteed in general.…”

Section: A Cutting-set Algorithmmentioning

confidence: 99%

“…Since the iterates lie in a compact set, the result holds for any sequence of iterates generated by the algorithm. 12 While global optimality of the optimization step is assumed in [32], it is not necessary for the convergence of the algorithm and the feasibility of its limit point. This is also shown in the proof of [41, Theorem 2.1].…”

Section: Appendix C Proof Of Propositionmentioning

confidence: 99%

“…• We propose an algorithm based on the cutting-set method [32], which solves the problem by alternating between an optimization step: where a solution is obtained w.r.t a finite subset of the uncertainty region, and a pessimization step: where the subset is updated through worst-case analysis. Contrary to works adopting this method [10], [33]- [35], we avoid conservative approximations used to convexify the optimization step, and we solve the pessimization step exactly, and hence guarantee convergence to a robust solution of the original semi-infinite problem.…”

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confidence: 99%

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Robust Transmission in Downlink Multiuser MISO Systems: A Rate-Splitting Approach

Joudeh

Clerckx

2016

IEEE Trans. Signal Process.

201

171

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Abstract-We consider a downlink multiuser MISO system with bounded errors in the Channel State Information at the Transmitter (CSIT). We first look at the robust design problem of achieving max-min fairness amongst users (in the worstcase sense). Contrary to the conventional approach adopted in literature, we propose a rather unorthodox design based on a Rate-Splitting (RS) strategy. Each user's message is split into two parts, a common part and a private part. All common parts are packed into one super common message encoded using a public codebook, while private parts are independently encoded. The resulting symbol streams are linearly precoded and simultaneously transmitted, and each receiver retrieves its intended message by decoding both the common stream and its corresponding private stream. For CSIT uncertainty regions that scale with SNR (e.g. by scaling the number of feedback bits), we prove that a RS-based design achieves higher max-min (symmetric) Degrees of Freedom (DoF) compared to conventional designs (NoRS). For the special case of non-scaling CSIT (e.g. fixed number of feedback bits), and contrary to NoRS, RS can achieve a non-saturating max-min rate. We propose a robust algorithm based on the cutting-set method coupled with the Weighted Minimum Mean Square Error (WMMSE) approach, and we demonstrate its performance gains over state-of-the art designs. Finally, we extend the RS strategy to address the Quality of Service (QoS) constrained power minimization problem, and we demonstrate significant gains over NoRS-based designs.Index Terms-MISO-BC, degrees of freedom, linear precoding, max-min fairness, quality-of-service, robust optimization.

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Section: Cutting-set Methodsmentioning

confidence: 99%

Section: A Cutting-set Algorithmmentioning

confidence: 99%

Section: Appendix C Proof Of Propositionmentioning

confidence: 99%

mentioning

confidence: 99%

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Robust Transmission in Downlink Multiuser MISO Systems: A Rate-Splitting Approach

Joudeh

Clerckx

2016

IEEE Trans. Signal Process.

201

171

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“…Our algorithm is essentially an instantiation of the general method presented in [23]; we refer the interested reader to this paper for a theoretical discussion of the fundamental properties of the approach.…”

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confidence: 99%

Computation of Worst Operation Scenarios Under Uncertainty for Static Security Management

Capitanescu

Wehenkel

2013

IEEE Trans. Power Syst.

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Abstract-This paper deals with day-ahead static security assessment with respect to a postulated set of contingencies while taking into account uncertainties about the next day system conditions. We propose a heuristic approach to compute the worst-case under operation uncertainty for a contingency with respect to overloads. We formulate this problem as a non-convex nonlinear bilevel program that we solve approximately by a heuristic approach which relies on the solution of successive optimal power flow (OPF) and security-constrained optimal power flow (SCOPF) problems of a special type. The method aims at revealing those combinations of uncertainties and contingencies for which the best combination of preventive and corrective actions would not suffice to ensure security. Extensive numerical results on a small, a medium, and a very large system prove the interest of the approach.Index Terms-Bilevel programming, operation under uncertainty, optimal power flow, security-constrained optimal power flow, worst-case analysis. NOMENCLATUREIn the paper vectors are written using bold characters. A. SetsSet of power flow equations in pre-contingency state. Set of power flow equations after contingency .Set of operating limits in pre-contingency state.Set of operating limits after contingency .Set of postulated contingencies.Set of violated constraints.Set of problematic constraints.Union of all sets of problematic constraints.Set of problematic patterns.

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A generalized cutting‐set approach for nonlinear robust optimization in process systems engineering

et al. 2021

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We propose a novel computational framework for the robust optimization of highly nonlinear, non‐convex models that possess uncertainty in their parameter data. The proposed method is a generalization of the robust cutting‐set algorithm that can handle models containing irremovable equality constraints, as is often the case with models in the process systems engineering domain. Additionally, we accommodate general forms of decision rules to facilitate recourse in second‐stage (control) variables. In particular, we compare and contrast the use of various types of decision rules, including quadratic ones, which we show in certain examples to be able to decrease the overall price of robustness. Our proposed approach is demonstrated on three process flow sheet models, including a relatively complex model for amine‐based CO2 capture. We thus verify that the generalization of the robust cutting‐set algorithm allows for the facile identification of robust feasible designs for process systems of practical relevance.

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Cutting-set methods for robust convex optimization with pessimizing oracles

Cited by 122 publications

References 91 publications

Robust Transmission in Downlink Multiuser MISO Systems: A Rate-Splitting Approach

Robust Transmission in Downlink Multiuser MISO Systems: A Rate-Splitting Approach

Computation of Worst Operation Scenarios Under Uncertainty for Static Security Management

A generalized cutting‐set approach for nonlinear robust optimization in process systems engineering

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