Global Order-Value Optimization by means of a Multistart Harmonic Oscillator Tunneling Strategy

Andreani, Roberto; Martínez, José Mário; Salvatierra, Mário; Yano, Flávio

doi:10.1007/0-387-30528-9_13

Cited by 3 publications

(5 citation statements)

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“…On the other hand, in the case that p r, the LOVO problem is a tool for finding Hidden Patterns in situations where a lot of wrong observations are mixed with a small number of correct data [7].…”

Section: Introductionmentioning

confidence: 99%

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Low Order-Value Optimization and applications

et al. 2008

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Given r real functions F 1 (x), . . . , F r (x) and an integer p between 1 and r, the Low OrderValue Optimization problem (LOVO) consists of minimizing the sum of the functions that take the p smaller values. If (y 1 , . . . , y r ) is a vector of data and T (x, t i ) is the predicted value of the observation i with the parameters x ∈ IR n , it is natural to define F i (x) = (T (x, t i ) − y i ) 2 (the quadratic error at observation i under the parameters x). When p = r this LOVO problem coincides with the classical nonlinear least-squares problem. However, the interesting situation is when p is smaller than r. In that case, the solution of LOVO allows one to discard the influence of an estimated number of outliers. Thus, the LOVO problem is an interesting tool for robust estimation of parameters of nonlinear models. When p r the LOVO problem may be used to find hidden structures in data sets. One of the best succeeded applications include the Protein Alignment problem. Fully documented algorithms for this application are available at www.ime.unicamp.br/∼martinez/lovoalign.In this paper optimality conditions are discussed, algorithms for solving the LOVO problem are introduced and convergence theorems are proved. Finally, numerical experiments are presented.

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Section: Introductionmentioning

confidence: 99%

“…Therefore, in most applications, global optimization tools are necessary for obtaining suitable initial points. In [7] a space-filling curve method was suggested for obtaining initial approximations when the original OVO is applied to Hidden Pattern problems. Specific problems need particular heuristics for finding initial points.…”

Section: Introductionmentioning

confidence: 99%

Low Order-Value Optimization and applications

et al. 2008

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“…O dado foi modelado usando o pacote Seis88 ( [42]). Nós aplicamos o Algoritmo Global para cada par (x 0 , t 0 ), com x 0 ∈ [3,7] km e incremento ∆x 0 = 25 m, e t 0 ∈ [0, 4] s com amostra de tempo ∆t 0 = 0.04 s, v 0 = 2 km/s. Portanto, para resolver o problema CRS fizemos 161 × 101 = 16261 chamadas do algoritmo.…”

Section: Experimentos Numéricosunclassified

“…A Otimização do Valor Ordenado é relevante, não somente por suas aplicações na área financeira, mas também por sua aplicação na estimação robusta e análise de dados [3]. Além disso, é um problema desafiador de otimização não-suave e global.…”

Section: Conclusõesunclassified

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Otimização global usando trajetorias densas e aplicações

Salvatierra¹,

Andreani²

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In this work a new global optimization method is defined combining deterministic and stochastic ideas. For this, we use a strategy to escape of local minimums established in following the trajectory of the Lissajous curve, a dense and smooth curve in an limited box Ω.The global algorithm is applied in a geophysical problem, known as the Common Reflection Surface (CRS) problem, and in the problem to find hidden patterns.Also we present a quasi-Newton method for the OVO problem that generalizes the Cauchy local method (used here as local method to find hidden patterns), and prove its superlinear and quadratic convergence. This new method is applied to a Brazilian variation of the Stiglitz's Ideal Banking System.

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