Journal ArticleDOI
Robust solutions to conic quadratic problems and their applications
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In this article, an approximate robust counterpart is formulated for the case where both sides of the constraint depend on the same perturbations, and the perturbation belongs to an uncertainty set which is an intersection of ellipsoids.Abstract:
This paper deals with uncertain conic quadratic constraints An approximate robust counterpart is formulated for the case where both sides of the constraint depend on the same perturbations, and the perturbations belong to an uncertainty set which is an intersection of ellipsoids Examples to problems in which such constraints occur are presented and solvedread more
Citations
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Recent advances in robust optimization: An overview☆
TL;DR: An overview of developments in robust optimization since 2007 is provided to give a representative picture of the research topics most explored in recent years, highlight common themes in the investigations of independent research teams and highlight the contributions of rising as well as established researchers both to the theory of robust optimization and its practice.
Journal ArticleDOI
Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles
TL;DR: A comprehensive review of Uncertainty-Based Multidisciplinary Design Optimization (UMDO) theory and the state of the art in UMDO methods for aerospace vehicles is presented.
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Tractable approximate robust geometric programming
TL;DR: To overcome the “curse of dimensionality” that arises in directly approximating the nonlinear constraint functions in the original robust GP, it is shown how to find globally optimal PWL approximations of these bivariate constraint functions.
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A modified Benders decomposition method for efficient robust optimization under interval uncertainty
TL;DR: The overall objective in this paper is to develop an efficient robust optimization method that is scalable and does not contain nested optimization and current results show that the approach is able to numerically obtain a locally optimal robust solution to problems with quasi-convex constraints and an approximate locally optimal resilient solution to general nonlinear optimization problems.
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Interval Uncertainty-Based Robust Optimization for Convex and Non-Convex Quadratic Programs with Applications in Network Infrastructure Planning
TL;DR: The results show that the computational effort of the proposed approach for finding robust optimum solutions to linear and quadratic programming problems with interval uncertainty is comparable to or even better than that of deterministic problems in some cases.
References
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Journal ArticleDOI
Robust Convex Optimization
Aharon Ben-Tal,Arkadi Nemirovski +1 more
TL;DR: If U is an ellipsoidal uncertainty set, then for some of the most important generic convex optimization problems (linear programming, quadratically constrained programming, semidefinite programming and others) the corresponding robust convex program is either exactly, or approximately, a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods.
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Applications of second-order cone programming
TL;DR: In this paper, an efficient primal-dual interior-point method for solving second-order cone programs (SOCP) is presented. But it is not a generalization of interior point methods for convex problems.
Journal ArticleDOI
Robust optimization – methodology and applications
Aharon Ben-Tal,Arkadi Nemirovski +1 more
TL;DR: The study reveals that the feasibility properties of the usual solutions of real world LPs can be severely affected by small perturbations of the data and that the RO methodology can be successfully used to overcome this phenomenon.
Journal ArticleDOI
Robust Solutions to Least-Squares Problems with Uncertain Data
Laurent El Ghaoui,Hervé Lebret +1 more
TL;DR: This work considers least-squares problems where the coefficient matrices A,b are unknown but bounded and minimize the worst-case residual error using (convex) second-order cone programming, yielding an algorithm with complexity similar to one singular value decomposition of A.
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Robust portfolio selection problems
Donald Goldfarb,Garud Iyengar +1 more
TL;DR: This paper introduces "uncertainty structures" for the market parameters and shows that the robust portfolio selection problems corresponding to these uncertainty structures can be reformulated as second-order cone programs and, therefore, the computational effort required to solve them is comparable to that required for solving convex quadratic programs.