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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TL;DR: A new scenario reduction heuristic named forward selection in wait-and-see clusters (FSWC) is test in the context of long-term power generation expansion planning to mitigate the computational complexity of the widely-used forward selection heuristic for scenario reduction.
129 citations
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TL;DR: A review of the methods for global optimization reveals that most methods have been developed for unconstrained problems and need to be extended to general constrained problems because most of the engineering applications have constraints.
Abstract: A review of the methods for global optimization reveals that most methods have been developed for unconstrained problems. They need to be extended to general constrained problems because most of the engineering applications have constraints. Some of the methods can be easily extended while others need further work. It is also possible to transform a constrained problem to an unconstrained one by using penalty or augmented Lagrangian methods and solve the problem that way. Some of the global optimization methods find all the local minimum points while others find only a few of them. In any case, all the methods require a very large number of calculations. Therefore, the computational effort to obtain a global solution is generally substantial. The methods for global optimization can be divided into two broad categories: deterministic and stochastic. Some deterministic methods are based on certain assumptions on the cost function that are not easy to check. These methods are not very useful since they are not applicable to general problems. Other deterministic methods are based on certain heuristics which may not lead to the true global solution. Several stochastic methods have been developed as some variation of the pure random search. Some methods are useful for only discrete optimization problems while others can be used for both discrete and continuous problems. Main characteristics of each method are identified and discussed. The selection of a method for a particular application depends on several attributes, such as types of design variables, whether or not all local minima are desired, and availability of gradients of all the functions.
129 citations
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01 Dec 1972
TL;DR: In this paper, a closed-loop control of a discrete-time linear system with possibly time-varying random parameters in the presence of input and output noise is presented.
Abstract: A new method is presented for controlling a discrete-time linear system with possibly time-varying random parameters in the presence of input and output noise. The cost is assumed to be quadratic in the state and control. Previous algorithms for the above problem when the system had both zeros and poles unknown were of the open-loop feedback type, i.e., they did not take into account that future observations will be made. Therefore, even though these schemes were adaptive, their learning was "accidental." In contrast to this, the new approach uses an expression of the optimal cost-to-go that exhibits the dual purpose of the control, i.e., learning and control. The effect of the present control on the future estimation ("learning") appears explicitly in the cost used in the stochastic dynamic programming equation. The resulting sequence of controls, which is of the closed-loop type, is shown via simulations to appropriately divide its energy between the learning and the control purposes. Therefore, this control is called actively adaptive because it regulates the speed and amount of learning as required by the performance index. The simulations on a third-order system with six unknown parameters also demonstrate the computational feasibility of the proposed algorithm.
129 citations
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07 Jun 2004TL;DR: In this paper, the authors studied the design of approximation algorithms for stochastic combinatorial optimization problems, and formulated the problems in the framework of two-staged optimization and provided nearly tight approximations.
Abstract: We study the design of approximation algorithms for stochastic combinatorial optimization problems. We formulate the problems in the framework of two-stage stochastic optimization, and provide nearly tight approximations. Our problems range from the simple (shortest path, vertex cover, bin packing) to complex (facility location, set cover), and contain representatives with different approximation ratios.
129 citations
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TL;DR: This model considers several multiperiod portfolio optimization models where the market consists of a riskless asset and several risky assets and the stochastic evolution of the market is described by a Markov chain with perfectly observable states.
128 citations