This paper converts the robust linear programming under the polyhedral uncertainty set to standard linearprogramming. After eliminating the parameter uncertainty, we design a projection neural network to address the ...
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This paper converts the robust linear programming under the polyhedral uncertainty set to standard linearprogramming. After eliminating the parameter uncertainty, we design a projection neural network to address the problem. The equilibrium point of the neural network model is theoretically proved to be stable in the Lyapunov sense and globally convergent to the optimal solution to robust linear programming. Two numerical examples are provided to illustrate the validity and performance of the proposed approach.
In this paper we consider a network of processors aiming at cooperatively solving linearprogramming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set....
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In this paper we consider a network of processors aiming at cooperatively solving linearprogramming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set....
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In this paper we consider a network of processors aiming at cooperatively solving linearprogramming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a randomized, distributed algorithm working under time-varying, asynchronous and directed communication topology. The algorithm is based on a local computation and communication paradigm. At each communication round, nodes perform two updates: (i) a verification in which they check in a randomized setup the robust feasibility (and hence optimality) of the candidate optimal point, and (ii) an optimization step in which they exchange their candidate bases (minimal sets of active constraints) with neighbors and locally solve an optimization problem whose constraint set includes: a sampled constraint violating the candidate optimal point (if it exists), agent's current basis and the collection of neighbor's basis. As main result, we show that if a processor successfully performs the verification step for a sufficient number of communication rounds, it can stop the algorithm since a consensus has been reached. The common solution is with high confidence feasible (and hence optimal) for the entire set of uncertainty except a subset having arbitrary small probability measure. We show the effectiveness of the proposed distributed algorithm on a multi-core platform in which the nodes communicate asynchronously. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
This letter studies formal synthesis of control policies for continuous-state MDPs. In the quest to satisfy complex combinations of probabilistic temporal logic specifications, we derive a robustlinear program for po...
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This letter studies formal synthesis of control policies for continuous-state MDPs. In the quest to satisfy complex combinations of probabilistic temporal logic specifications, we derive a robustlinear program for policy synthesis that is solved on a finite-state approximation of the system and is then refined back to a policy for the original system. This linearprogramming approach leverages occupation measures and enables the multi-objective optimizations needed to handle more complex probabilistic specifications.
We first show that the closedness of the characteristic cone of the constraint system of a parametric robustlinear optimization problem is a necessary and sufficient condition for each robustlinear program with the ...
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We first show that the closedness of the characteristic cone of the constraint system of a parametric robustlinear optimization problem is a necessary and sufficient condition for each robustlinear program with the finite optimal value to admit exact semidefinite linearprogramming relaxations. We then provide the weakest regularity condition that guarantees exact second-order cone programming relaxations for parametric robustlinear programs. (C) 2019 Elsevier B.V. All rights reserved.
This article focuses on a robust optimization of an aircraft preliminary design under operational constraints. According to engineers' know-how, the aircraft preliminary design problem can be modelled as an uncert...
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This article focuses on a robust optimization of an aircraft preliminary design under operational constraints. According to engineers' know-how, the aircraft preliminary design problem can be modelled as an uncertain optimization problem whose objective (the cost or the fuel consumption) is almost affine, and whose constraints are convex. It is shown that this uncertain optimization problem can be approximated in a conservative manner by an uncertain linear optimization program, which enables the use of the techniques of robust linear programming of Ben-Tal, ElGhaoui, and Nemirovski [robust Optimization, Princeton University Press, 2009]. This methodology is then applied to two real cases of aircraft design and numerical results are presented.
In this paper,we aim to solve an inverse robust optimization problem,in which the parameters in both the objective function and the robust constraint set need to be adjusted as little as possible so that a known feasi...
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In this paper,we aim to solve an inverse robust optimization problem,in which the parameters in both the objective function and the robust constraint set need to be adjusted as little as possible so that a known feasible solution becomes the optimal *** formulate this inverse problem as a minimization problem with a linear equality constraint,a second-order cone complementarity constraint and a linear complementarity constraint.A perturbation approach is constructed to solve the inverse *** inexact Newton method with Armijo line search is applied to solve the perturbed ***,the numerical results are reported to show the effectiveness of the approach.
In this paper, our major theme is a unifying framework for duality in robust linear programming. We show that there are two pair of dual programs allied with a robustlinear program;one in which the primal is construc...
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In this paper, our major theme is a unifying framework for duality in robust linear programming. We show that there are two pair of dual programs allied with a robustlinear program;one in which the primal is constructed to be "ultra-conservative" and one in which the primal is constructed to be "ultra-optimistic." Furthermore, as one would expect, if the uncertainly in the primal is row-based, the corresponding uncertainty in the dual is column-based, and vice-versa. Several examples are provided that illustrate the properties of these primal and dual models. A second theme of the paper is about modeling in robust linear programming. We replace the ordinary activity vectors (points) and right-hand sides with well-known geometric objects such as hyper-rectangles, parallel line segments and hyper-spheres. In this manner, imprecision and uncertainty can be explicitly modeled as an inherent characteristic of the model. This is in contrast to the usual approach of using vectors to model activities and/or constraints and then, subsequently, imposing some further constraints in the model to accommodate imprecision and uncertainties. The unifying duality structure is then applied to these models to understand and interpret the marginal prices. The key observation is that the optimal solutions to these dual problems are comprised of two parts: a traditional "centrality" component along with a "robustness" component. (C) 2012 Elsevier Ltd, All rights reserved.
Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply rates are em...
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Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply rates are employed here for robustness and performance analysis using L-1-gain and L-gain. robust stability analysis is performed using integral linear constraints for which several classes of uncertainties are discussed. The approach is then extended to robust stabilization and performance optimization. The obtained results are expressed in terms of robust linear programming problems that are equivalently turned into finite dimensional ones using Handelman's theorem. Several examples are provided for illustration. Copyright (c) 2012 John Wiley & Sons, Ltd.
As shown in previous work, robust linear programming problems featuring polyhedral right-hand side (RHS) uncertainty (a) arise in many practical applications;(b) frequently lead to robust equivalents belonging to the ...
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As shown in previous work, robust linear programming problems featuring polyhedral right-hand side (RHS) uncertainty (a) arise in many practical applications;(b) frequently lead to robust equivalents belonging to the class of strongly NP-hard problems. In the present paper the case of ellipsoidal RHS uncertainty is investigated and similar complexity results are shown to hold even when restricting to simplified specially structured problems related to robust production planning under uncertain customer requirements. The proof is based on a reduction which significantly differs from the one used in the case of polyhedral RHS uncertainty.
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