Topic
Stochastic programming
About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.
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12 Dec 2011TL;DR: This work shows n-node architectures whose optimization error in stochastic problems-in spite of asynchronous delays-scales asymptotically as O(1/√nT) after T iterations, known to be optimal for a distributed system with n nodes even in the absence of delays.
Abstract: We analyze the convergence of gradient-based optimization algorithms whose updates depend on delayed stochastic gradient information. The main application of our results is to the development of distributed minimization algorithms where a master node performs parameter updates while worker nodes compute stochastic gradients based on local information in parallel, which may give rise to delays due to asynchrony. Our main contribution is to show that for smooth stochastic problems, the delays are asymptotically negligible. In application to distributed optimization, we show n-node architectures whose optimization error in stochastic problems—in spite of asynchronous delays—scales asymptotically as O(1/√nT), which is known to be optimal even in the absence of delays.
117 citations
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13 May 2009TL;DR: An asynchronous algorithm that is motivated by random gossip schemes where each agent has a local Poisson clock and it is proved that the gradients converge to zero with probability 1 and the iterates converge to an optimal solution almost surely.
Abstract: We consider a distributed multi-agent network system where the goal is to minimize an objective function that can be written as the sum of component functions, each of which is known (with stochastic errors) to a specific network agent. We propose an asynchronous algorithm that is motivated by a random gossip scheme where each agent has a local Poisson clock. At each tick of its local clock, the agent averages its estimate with a randomly chosen neighbor and adjusts the average using the gradient of its local function that is computed with stochastic errors.We investigate the convergence properties of the algorithm for two different classes of functions: differentiable but not necessarily convex and convex but not necessarily differentiable.
117 citations
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TL;DR: The implementation results of the proposed approach for a realistic-scale sawmill example highlights the significance of using robust optimization in generating more robust production plans in the uncertain environments compared with stochastic programming.
116 citations
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TL;DR: This paper proposes a new distance-based distributionally robust unit commitment model via Kullback–Leibler (KL) divergence, considering volatile wind power generation, and proposes a two-level decomposition method and an iterative algorithm to address the RDB-DRUC model.
Abstract: This paper proposes a new distance-based distributionally robust unit commitment (DB-DRUC) model via Kullback–Leibler (KL) divergence, considering volatile wind power generation. The objective function of the DB-DRUC model is to minimize the expected cost under the worst case wind distributions restricted in an ambiguity set. The ambiguity set is a family of distributions within a fixed distance from a nominal distribution. The distance between two distributions is measured by KL divergence. The DB-DRUC model is a “min-max-min” programming model; thus, it is intractable to solve. Applying reformulation methods and stochastic programming technologies, we reformulate this “min-max-min” DB-DRUC model into a one-level model, referred to as the reformulated DB-DRUC (RDB-DRUC) model. Using the generalized Benders decomposition, we then propose a two-level decomposition method and an iterative algorithm to address the RDB-DRUC model. The iterative algorithm for the RDB-DRUC model guarantees global convergence within finite iterations. Case studies are carried out to demonstrate the effectiveness, global optimality, and finite convergence of a proposed solution strategy.
116 citations
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TL;DR: The simulation results confirm that the Benders decomposing method offers extremely high levels of accuracy and power in solving the complex model of coordinated planning and operation problem in the presence of uncertainties and numerous decision variables.
116 citations