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JournalISSN: 0926-6003

Computational Optimization and Applications 

Springer Science+Business Media
About: Computational Optimization and Applications is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Optimization problem & Mathematics. It has an ISSN identifier of 0926-6003. Over the lifetime, 1956 publications have been published receiving 58785 citations.


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Journal ArticleDOI
TL;DR: Two new versions of forward and backward type algorithms are presented for computing such optimally reduced probability measures approximately for convex stochastic programs with an (approximate) initial probability distribution P having finite support supp P.
Abstract: We consider convex stochastic programs with an (approximate) initial probability distribution P having finite support supp P, i.e., finitely many scenarios. The behaviour of such stochastic programs is stable with respect to perturbations of P measured in terms of a Fortet-Mourier probability metric. The problem of optimal scenario reduction consists in determining a probability measure that is supported by a subset of supp P of prescribed cardinality and is closest to P in terms of such a probability metric. Two new versions of forward and backward type algorithms are presented for computing such optimally reduced probability measures approximately. Compared to earlier versions, the computational performance (accuracy, running time) of the new algorithms has been improved considerably. Numerical experience is reported for different instances of scenario trees with computable optimal lower bounds. The test examples also include a ternary scenario tree representing the weekly electrical load process in a power management model.

851 citations

Journal ArticleDOI
TL;DR: The authors summarizes the research on population-based probabilistic search algorithms based on modeling promising solutions by estimating their probability distribution and using the constructed model to guide the exploration of the search space.
Abstract: This paper summarizes the research on population-based probabilistic search algorithms based on modeling promising solutions by estimating their probability distribution and using the constructed model to guide the exploration of the search space. It settles the algorithms in the field of genetic and evolutionary computation where they have been originated, and classifies them into a few classes according to the complexity of models they use. Algorithms within each class are briefly described and their strengths and weaknesses are discussed.

734 citations

Journal ArticleDOI
TL;DR: This paper proves that the expansion and contraction steps of the Nelder-Mead simplex algorithm possess a descent property when the objective function is uniformly convex, and proposes an implementation in which the expansion, contraction, and shrink parameters depend on the dimension of the optimization problem.
Abstract: In this paper, we first prove that the expansion and contraction steps of the Nelder-Mead simplex algorithm possess a descent property when the objective function is uniformly convex. This property provides some new insights on why the standard Nelder-Mead algorithm becomes inefficient in high dimensions. We then propose an implementation of the Nelder-Mead method in which the expansion, contraction, and shrink parameters depend on the dimension of the optimization problem. Our numerical experiments show that the new implementation outperforms the standard Nelder-Mead method for high dimensional problems.

666 citations

Journal ArticleDOI
TL;DR: Numerical comparisons with MINOS and LANCELOT show that the interior-point algorithm for nonconvex nonlinear programming is efficient, and has the promise of greatly reducing solution times on at least some classes of models.
Abstract: The paper describes an interior-point algorithm for nonconvex nonlinear programming which is a direct extension of interior-point methods for linear and quadratic programming. Major modifications include a merit function and an altered search direction to ensure that a descent direction for the merit function is obtained. Preliminary numerical testing indicates that the method is robust. Further, numerical comparisons with MINOS and LANCELOT show that the method is efficient, and has the promise of greatly reducing solution times on at least some classes of models.

567 citations

Journal ArticleDOI
TL;DR: Smoothing methods are applied here to generate and solve an unconstrained smooth reformulation of the support vector machine for pattern classification using a completely arbitrary kernel, which converges globally and quadratically.
Abstract: Smoothing methods, extensively used for solving important mathematical programming problems and applications, are applied here to generate and solve an unconstrained smooth reformulation of the support vector machine for pattern classification using a completely arbitrary kernel. We term such reformulation a smooth support vector machine (SSVM). A fast Newton–Armijo algorithm for solving the SSVM converges globally and quadratically. Numerical results and comparisons are given to demonstrate the effectiveness and speed of the algorithm. On six publicly available datasets, tenfold cross validation correctness of SSVM was the highest compared with four other methods as well as the fastest. On larger problems, SSVM was comparable or faster than SVMlight (T. Joachims, in Advances in Kernel Methods—Support Vector Learning, MIT Press: Cambridge, MA, 1999), SOR (O.L. Mangasarian and David R. Musicant, IEEE Transactions on Neural Networks, vol. 10, pp. 1032–1037, 1999) and SMO (J. Platt, in Advances in Kernel Methods—Support Vector Learning, MIT Press: Cambridge, MA, 1999). SSVM can also generate a highly nonlinear separating surface such as a checkerboard.

565 citations

Performance
Metrics
No. of papers from the Journal in previous years
YearPapers
202352
2022122
2021100
202094
201993
201895