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  • Articles  (70)
  • Global optimization  (70)
  • Springer  (70)
  • American Chemical Society (ACS)
  • Cell Press
  • 1995-1999  (65)
  • 1980-1984  (5)
  • Mathematics  (70)
  • Economics  (3)
Collection
  • Articles  (70)
Source
Keywords
Publisher
  • Springer  (70)
  • American Chemical Society (ACS)
  • Cell Press
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Year
Topic
  • 1
    Electronic Resource
    Electronic Resource
    An adaptive stochastic global optimization algorithm for one-dimensional functions (1995)
    Springer
    Annals of operations research 58 (1995), S. 261-278 
    Details
    ISSN: 1572-9338
    Keywords: Global optimization ; Wiener process ; sequential stopping rules ; one-step look-ahead
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper a new algorithm is proposed, based upon the idea of modeling the objective function of a global optimization problem as a sample path from a Wiener process. Unlike previous work in this field, in the proposed model the parameter of the Wiener process is considered as a random variable whose conditional (posterior) distribution function is updated on-line. Stopping criteria for Bayesian algorithms are discussed and detailed proofs on finite-time stopping are provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02096402
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  • 2
    Electronic Resource
    Electronic Resource
    A Bayesian algorithm for global optimization (1984)
    Springer
    Annals of operations research 1 (1984), S. 111-128 
    Details
    ISSN: 1572-9338
    Keywords: Global optimization ; Bayesian nonparametric inference ; random distributions ; cluster analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A crucial step in global optimization algorithms based on random sampling in the search domain is decision about the achievement of a prescribed accuracy. In order to overcome the difficulties related to such a decision, the Bayesian Nonparametric Approach has been introduced. The aim of this paper is to show the effectiveness of the approach when an ad hoc clustering technique is used for obtaining promising starting points for a local search algorithm. Several test problems are considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01876142
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  • 3
    Electronic Resource
    Electronic Resource
    A survey on the global optimization problem: General theory and computational approaches (1984)
    Springer
    Annals of operations research 1 (1984), S. 87-110 
    Details
    ISSN: 1572-9338
    Keywords: Global optimization ; statistical optimization ; Bayesian statistics ; random search
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Several different approaches have been suggested for the numerical solution of the global optimization problem: space covering methods, trajectory methods, random sampling, random search and methods based on a stochastic model of the objective function are considered in this paper and their relative computational effectiveness is discussed. A closer analysis is performed of random sampling methods along with cluster analysis of sampled data and of Bayesian nonparametric stopping rules.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01876141
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  • 4
    Electronic Resource
    Electronic Resource
    Pure adaptive search for finite global optimization (1995)
    Springer
    Mathematical programming 69 (1995), S. 443-448 
    Details
    ISSN: 1436-4646
    Keywords: Global optimization ; Discrete optimization ; Algorithm complexity ; Random search ; Markov chains
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Pure Adaptive Search is a stochastic algorithm which has been analyzed for continuous global optimization. When a uniform distribution is used in PAS, it has been shown to have complexity which is linear in dimension. We define strong and weak variations of PAS in the setting of finite global optimization and prove analogous results. In particular, for then-dimensional lattice {1,⋯,k} n , the expected number of iterations to find the global optimum is linear inn. Many discrete combinatorial optimization problems, although having intractably large domains, have quite small ranges. The strong version of PAS for all problems, and the weak version of PAS for a limited class of problems, has complexity the order of the size of the range.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585570
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  • 5
    Electronic Resource
    Electronic Resource
    Global one-dimensional optimization using smooth auxiliary functions (1998)
    Springer
    Mathematical programming 81 (1998), S. 127-146 
    Details
    ISSN: 1436-4646
    Keywords: Global optimization ; Lipschitzean first derivatives ; Numerical algorithms ; Convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper new global optimization algorithms are proposed for solving problems where the objective function is univariate and has Lipschitzean first derivatives. To solve this problem, smooth auxiliary functions, which are adaptively improved during the course of the search, are constructed. Three new algorithms are introduced: the first used the exact a priori known Lipschitz constant for derivatives; the second, when this constant is unknown, estimates it during the course of the search and finally, the last method uses neither the exact global Lipschitz constant nor its estimate but instead adaptively estimates the local Lipschitz constants in different sectors of the search region during the course of optimization. Convergence conditions of the methods are investigated from a general viewpoint and some numerical results are also given. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584848
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  • 6
    Electronic Resource
    Electronic Resource
    Analytical solutions to the optimization of a quadratic cost function subject to linear and quadratic equality constraints (1996)
    Springer
    Applied mathematics & optimization 34 (1996), S. 161-182 
    Details
    ISSN: 1432-0606
    Keywords: Global optimization ; Quadratic cost ; Quadratic equality constraints ; Multivariate polynomials ; Resultants ; 49N99 ; 90C26 ; 90C30 ; 65K05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In the area of broad-band antenna array signal processing, the global minimum of a quadratic equality constrained quadratic cost minimization problem is often required. The problem posed is usually characterized by a large optimization space (around 50–90 tuples), a large number of linear equality constraints, and a few quadratic equality constraints each having very low rank quadratic constraint matrices. Two main difficulties arise in this class of problem. Firstly, the feasibility region is nonconvex and multiple local minima abound. This makes conventional numerical search techniques unattractive as they are unable to locate the global optimum consistently (unless a finite search area is specified). Secondly, the large optimization space makes the use of decision-method algorithms for the theory of the reals unattractive. This is because these algorithms involve the solution of the roots of univariate polynomials of order to the square of the optimization space. In this paper we present a new algorithm which exploits the structure of the constraints to reduce the optimization space to a more manageable size. The new algorithm relies on linear-algebra concepts, basic optimization theory, and a multivariate polynomial root-solving tool often used by decision-method algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01182622
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  • 7
    Electronic Resource
    Electronic Resource
    Metric unidimensional scaling and global optimization (1996)
    Springer
    Journal of classification 13 (1996), S. 3-18 
    Details
    ISSN: 1432-1343
    Keywords: Unidimensional scaling ; Seriation ; Local minima ; Global optimization ; Smoothing technique ; Multidimensional scaling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For the problem of metric unidimensional scaling, the number of local minima is estimated. For locating the globally optimal solution we develop an approach, called the “smoothing technique.” Although not guaranteed inevitably to locate the global optimum, the smoothing technique did so in all computational experiments where the global optimum was known.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01202579
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  • 8
    Electronic Resource
    Electronic Resource
    Outer approximation algorithm for nondifferentiable optimization problems (1984)
    Springer
    Journal of optimization theory and applications 42 (1984), S. 19-30 
    Details
    ISSN: 1573-2878
    Keywords: Global optimization ; nondifferentiable optimization ; Lipschitz continuous functions ; outer-approximation algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is known that the problem of minimizing a convex functionf(x) over a compact subsetX of ℝ n can be expressed as minimizing max{g(x, y)|y ∈X}, whereg is a support function forf[f(x) ≥g(x, y), for ally ∈X andf(x)=g(x, x)]. Standard outer-approximation theory can then be employed to obtain outer-approximation algorithms with procedures for dropping previous cuts. It is shown here how this methodology can be extended to nonconvex nondifferentiable functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934131
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  • 9
    Electronic Resource
    Electronic Resource
    Outer approximation algorithm for nondifferentiable optimization problems (1984)
    Springer
    Journal of optimization theory and applications 44 (1984), S. 365-365 
    Details
    ISSN: 1573-2878
    Keywords: Global optimization ; nondifferentiable optimization ; Lipschitz continuous functions ; outer-approximation algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Omissions from the list of references of Ref. 1 are corrected.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935443
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  • 10
    Electronic Resource
    Electronic Resource
    Deletion-by-infeasibility rule for DC-constrained global optimization (1995)
    Springer
    Journal of optimization theory and applications 84 (1995), S. 443-455 
    Details
    ISSN: 1573-2878
    Keywords: Global optimization ; nonconvex programming ; mathematical programming ; DC-programming ; branch-and-bound methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In Ref. 1, a general class of branch-and-bound methods was proposed by Horst for solving global optimization problems. One of the main contributions of Ref. 1 was the opportunity of handling partition elements whose feasibility is not known. Deletion-by-infeasibility rules were presented for problems where the feasible set is convex, is defined by finitely many convex and reverse convex constraints, or is defined by Lipschitzian inequalities. In this note, we propose a new deletion-by-infeasibility rule for problems whose feasible set is defined by functions representable as differences of convex functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02192125
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