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Computing the Global Optimum . . .
, 2008
"... Let f be a polynomial in Q[X1,..., Xn] of degree D. We provide an efficient algorithm in practice to compute the global supremum supx∈Rn f(x) of f (or its infimum inf x∈Rn f(x)). The complexity of our method is bounded by D O(n). In a probabilistic model, a more precise result yields a complexity bo ..."
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critical values of the mapping x → f(x), i.e. the set of points {c ∈ C | ∃(xℓ)ℓ∈N ⊂ C n f(xℓ) → c, ||xℓ||||dxℓf| | → 0 when ℓ → ∞}. We prove that the global optimum of f lies in its set of generalized critical values and provide an efficient way of deciding which value is the global optimum.
Globally Optimum Multiple Object Tracking
"... Robust and accurate tracking of multiple objects is a key challenge in video surveillance. Tracking algorithms generally suffer from either one or more of the following problems, excluding detection errors. First, objects can be incorrectly interpreted as one of the other objects in the scene. Secon ..."
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Cited by 3 (0 self)
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. Second, interactions between objects, such as occlusions, may cause tracking errors. Third, globally-optimum tracking is hard to achieve since the combinatorial assignment problem is NP-Complete. We present a modified Multiple-Hypothesis Tracking algorithm, MHT, for globally optimum tracking of moving
Bethe Bounds and Approximating the Global Optimum
"... Abstract—Inference in general Markov random fields (MRFs) is NP-hard, though identifying the maximum a posteriori (MAP) configuration of pairwise MRFs with submodular cost functions is efficiently solvable using graph cuts. Marginal inference, however, even for this restricted class, is in #P. We pr ..."
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Cited by 9 (8 self)
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pseudo-marginals in the associative case we present a polynomial time approximation scheme for global optimization provided the maximum degree is O(log n), anddiscussseveralextensions. I.
Global Optimum Protein Threading with Gapped Alignment and Empirical Pair Score Functions
- J. Mol. Biol
, 1996
"... We describe a branch-and-bound search algorithm for finding the exact global optimum gapped sequencestructure alignment ("threading") between a protein sequence and a protein core or structural model, using an arbitrary amino acid pair score function (e.g., contact potentials, knowledge-ba ..."
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Cited by 69 (5 self)
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We describe a branch-and-bound search algorithm for finding the exact global optimum gapped sequencestructure alignment ("threading") between a protein sequence and a protein core or structural model, using an arbitrary amino acid pair score function (e.g., contact potentials, knowledge
Finding globally optimum solutions in antenna optimization problems
- IEEE International Symposium on Antennas and Propagation
, 2010
"... During the last decade, the unprecedented increase in the affordable computational power has strongly supported the development of optimization techniques for designing antennas. Among these techniques, genetic algorithm [1] and particle swarm optimization [2] could be mentioned. Most of these techn ..."
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Cited by 3 (2 self)
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During the last decade, the unprecedented increase in the affordable computational power has strongly supported the development of optimization techniques for designing antennas. Among these techniques, genetic algorithm [1] and particle swarm optimization [2] could be mentioned. Most of these techniques use physical dimensions of an antenna
Application of Chaos Induced Near-Resonance Dynamics to Locate the Global Optimum of Functions
, 2001
"... The problem of locating the global optimum of functions is studied in a dynamic setting. The dynamics of simple multistable systems under the influence of chaotic forcing is investigated. When the magnitude of the forcing signal decays slowly, it is shown that the system attains an equilibrium state ..."
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The problem of locating the global optimum of functions is studied in a dynamic setting. The dynamics of simple multistable systems under the influence of chaotic forcing is investigated. When the magnitude of the forcing signal decays slowly, it is shown that the system attains an equilibrium
Exact computation of the fitness-distance correlation for pseudoboolean functions with one global optimum
- Evolutionary Computation in Combinatorial Optimization, volume 7245 of Lecture Notes in Computer Science
, 2012
"... Abstract. Landscape theory provides a formal framework in which combinatorial optimization problems can be theoretically characterized as a sum of a special kind of landscapes called elementary landscapes. The decomposition of the objective function of a problem into its elementary components can b ..."
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Cited by 2 (1 self)
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be exploited to compute summary statistics. We present closed-form expressions for the fitness-distance correlation (FDC) based on the elementary landscape decomposition of the problems defined over binary strings in which the objective function has one global optimum. We present some theoretical results
A New Kind of Hopfield Networks for Finding Global Optimum
, 2005
"... Abstract — The Hopfield network has been applied to solve optimization problems over decades. However, it still has many limitations in accomplishing this task. Most of them are inherited from the optimization algorithms it implements. The computation of a Hopfield network, defined by a set of diffe ..."
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of difference equations, can easily be trapped into one local optimum or another, sensitive to initial conditions, perturbations, and neuron update orders. It doesn’t know how long it will take to converge, as well as if the final solution is a global optimum, or not. In this paper, we present a Hopfield
Dynamic Programming: Globally Optimum Selection of Storage Patterns Overview
"... This talk has two goals: a) A review of the fundamentals of dynamic programming, and an introduction to nonserial dynamic programming; b) An application of the techniques to some of the issues involved in the problem of determining globally optimum storage patterns. Dynamic Programming Dynamic progr ..."
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This talk has two goals: a) A review of the fundamentals of dynamic programming, and an introduction to nonserial dynamic programming; b) An application of the techniques to some of the issues involved in the problem of determining globally optimum storage patterns. Dynamic Programming Dynamic
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