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  • 1
    Electronic Resource
    Electronic Resource
    Concurrent stochastic methods for global optimization (1990)
    Springer
    Mathematical programming 46 (1990), S. 1-29 
    Details
    ISSN: 1436-4646
    Keywords: Global optimization ; concurrent ; parallel ; stochastic ; network of computers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The global optimization problem, finding the lowest minimizer of a nonlinear function of several variables that has multiple local minimizers, appears well suited to concurrent computation. This paper presents a new parallel algorithm for the global optimization problem. The algorithm is a stochastic method related to the multi-level single-linkage methods of Rinnooy Kan and Timmer for sequential computers. Concurrency is achieved by partitioning the work of each of the three main parts of the algorithm, sampling, local minimization start point selection, and multiple local minimizations, among the processors. This parallelism is of a coarse grain type and is especially well suited to a local memory multiprocessing environment. The paper presents test results of a distributed implementation of this algorithm on a local area network of computer workstations. It also summarizes the theoretical properties of the algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585724
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  • 2
    Electronic Resource
    Electronic Resource
    Convergence rates of a global optimization algorithm (1992)
    Springer
    Mathematical programming 54 (1992), S. 223-232 
    Details
    ISSN: 1436-4646
    Keywords: Global optimization ; Lipschitz functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents a best and worst case analysis of convergence rates for a deterministic global optimization algorithm. Superlinear convergence is proved for Lipschitz functions which are convex in the direction of the global maximum (concave in the direction of the global minimum). Computer results are given, which confirm the theoretical convergence rates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586051
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  • 3
    Electronic Resource
    Electronic Resource
    Global optimization and simulated annealing (1991)
    Springer
    Mathematical programming 50 (1991), S. 367-393 
    Details
    ISSN: 1436-4646
    Keywords: Global optimization ; continuous variables ; simulated annealing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we are concerned with global optimization, which can be defined as the problem of finding points on a bounded subset of ℝ n in which some real valued functionf assumes its optimal (maximal or minimal) value. We present a stochastic approach which is based on the simulated annealing algorithm. The approach closely follows the formulation of the simulated annealing algorithm as originally given for discrete optimization problems. The mathematical formulation is extended to continuous optimization problems, and we prove asymptotic convergence to the set of global optima. Furthermore, we discuss an implementation of the algorithm and compare its performance with other well-known algorithms. The performance evaluation is carried out for a standard set of test functions from the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01594945
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  • 4
    Electronic Resource
    Electronic Resource
    Global minimization by reducing the duality gap (1994)
    Springer
    Mathematical programming 63 (1994), S. 193-212 
    Details
    ISSN: 1436-4646
    Keywords: Global optimization ; nonconvex programming ; duality gap ; branch and bound method ; decomposition ; nonsmooth optimization ; pooling problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We derive a general principle demonstrating that by partitioning the feasible set, the duality gap, existing between a nonconvex program and its lagrangian dual, can be reduced, and in important special cases, even eliminated. The principle can be implemented in a Branch and Bound algorithm which computes an approximate global solution and a corresponding lower bound on the global optimal value. The algorithm involves decomposition and a nonsmooth local search. Numerical results for applying the algorithm to the pooling problem in oil refineries are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582066
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  • 5
    Electronic Resource
    Electronic Resource
    An analytical approach to global optimization (1991)
    Springer
    Mathematical programming 52 (1991), S. 227-254 
    Details
    ISSN: 1436-4646
    Keywords: Global optimization ; analytical methods ; computer algebra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Global optimization problems with a few variables and constraints arise in numerous applications but are seldom solved exactly. Most often only a local optimum is found, or if a global optimum is detected no proof is provided that it is one. We study here the extent to which such global optimization problems can be solved exactly using analytical methods. To this effect, we propose a series of tests, similar to those of combinatorial optimization, organized in a branch-and-bound framework. The first complete solution of two difficult test problems illustrates the efficiency of the resulting algorithm. Computational experience with the programbagop, which uses the computer algebra systemmacsyma, is reported on. Many test problems from the compendiums of Hock and Schittkowski and others sources have been solved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582889
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  • 6
    Electronic Resource
    Electronic Resource
    Optimal and sub-optimal stopping rules for the Multistart algorithm in global optimization (1992)
    Springer
    Mathematical programming 57 (1992), S. 445-458 
    Details
    ISSN: 1436-4646
    Keywords: Global optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper the problem of stopping the Multistart algorithm for global optimization is considered. The algorithm consists of repeatedly performing local searches from randomly generated starting points. The crucial point in this algorithmic scheme is the development of a stopping criterion; the approach analyzed in this paper consists in stopping the sequential sampling as soon as a measure of the trade-off between the cost of further local searches is greater than the expected benefit, i.e. the possibility of discovering a better optimum. Stopping rules are thoroughly investigated both from a theoretical point of view and from a computational one via extensive simulation. This latter clearly shows that the simple1-step look ahead rule may achieve surprisingly good results in terms of computational cost vs. final accuracy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581094
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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    Parallel computing in nonconvex programming (1993)
    Springer
    Annals of operations research 43 (1993), S. 87-107 
    Details
    ISSN: 1572-9338
    Keywords: Global optimization ; parallel computing ; minimum-concave cost network flow problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper, we are concerned with the development of parallel algorithms for solving some classes of nonconvex optimization problems. We present an introductory survey of parallel algorithms that have been used to solve structured problems (partially separable, and large-scale block structured problems), and algorithms based on parallel local searches for solving general nonconvex problems. Indefinite quadratic programming posynomial optimization, and the general global concave minimization problem can be solved using these approaches. In addition, for the minimum concave cost network flow problem, we are going to present new parallel search algorithms for large-scale problems. Computational results of an efficient implementation on a multi-transputer system will be presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02024487
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  • 9
    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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  • 10
    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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