Topic
Discrete optimization
About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.
Papers published on a yearly basis
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15 Mar 2016TL;DR: The proposed algorithms are proved to be effective for those heterogeneous nonlinear agents to achieve the optimization solution in the semi-global sense, even with the exponential convergence rate.
Abstract: In this paper, distributed optimization control for a group of autonomous Lagrangian systems is studied to achieve an optimization task with local cost functions. To solve the problem, two continuous-time distributed optimization algorithms are designed for multiple heterogeneous Lagrangian agents with uncertain parameters. The proposed algorithms are proved to be effective for those heterogeneous nonlinear agents to achieve the optimization solution in the semi-global sense, even with the exponential convergence rate. Moreover, simulation adequately illustrates the effectiveness of our optimization algorithms.
68 citations
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TL;DR: In this article, the authors present an overview of the recent advances in deterministic global optimization approaches and their applications in the areas of process design and control, focusing on global optimization methods for (a) twice-differentiable constrained nonlinear optimization problems, (b) mixed-integer nonlinear optimisation problems, and (c) locating all solutions of nonlinear systems of equations.
68 citations
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01 Dec 2003TL;DR: The paper demonstrates how discrete exterior calculus tools may be useful in computer vision and graphics and shows some example applications using variational problems from computer graphics and mechanics to demonstrate that formulating the problem discretely and using discrete methods for solution can lead to efficient algorithms.
Abstract: The paper demonstrates how discrete exterior calculus (DEC) tools may be useful in computer vision and graphics. A variational approach provides a link with mechanics. Our development of DEC includes discrete differential forms, discrete vector fields and the operators acting on these. This development of a discrete calculus, when combined with the methods of discrete mechanics and other recent work is likely to have promising applications in a field like computer vision which offers such a rich variety of challenging variational problems to be solved computationally. As a specific example we consider the problem of template matching and show how numerical methods derived from a discrete exterior calculus are starting to play an important role in solving the equations of averaged template matching. We also show some example applications using variational problems from computer graphics and mechanics to demonstrate that formulating the problem discretely and using discrete methods for solution can lead to efficient algorithms.
67 citations
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TL;DR: In this paper, the authors present a counterexample to a previously stated result in this area, namely that the set of efficient solutions of the shortest path problem is connected, and also show that connectedness does not hold for another important problem in discrete multiple criteria optimization: the spanning tree problem.
67 citations
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01 Jan 1995TL;DR: Some authors use the acronym DEDS, for a discrete event dynamic system, rather than DES, to emphasize the fact that the behavior of such systems can, and usually will, change as time proceeds.
Abstract: The theory of Discrete Event Systems (DES) is a research area of current vitality The development of this theory is largely stimulated by discovering general principles which are (or are hoped to be) useful to a wide range of application domains In particular, technological and/or ‘man-made’ manufacturing systems, communication networks, transportation systems, and logistic systems, all fall within the class of DES There are two key features that characterize these systems First, their dynamics are event-driven as opposed to time-driven, ie, the behavior of a DES is governed only by occurrences of different types of events over time rather than by ticks of a clock Unlike conventional time-driven systems, the fact that time evolves in between event occurrences has no visible effect on the system Second, at least some of the natural variables required to describe a DES are discrete Examples of events include the pushing of a button or an unpredictable computer failure Examples of discrete variables involved in modelling a DES are descriptors of the state of a resource (eg, UP, DOWN, BUSY, IDLE) or (integer-valued) counters for the number of users waiting to be served by a resource Some authors use the acronym DEDS, for a discrete event dynamic system, rather than DES, to emphasize the fact that the behavior of such systems can, and usually will, change as time proceeds
67 citations