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  • Articles  (112)
  • Global optimization  (57)
  • 16W30  (55)
  • 1990-1994  (112)
  • 1965-1969
  • Mathematics  (112)
  • Architecture, Civil Engineering, Surveying
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  • Articles  (112)
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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
    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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  • 8
    Electronic Resource
    Electronic Resource
    Quantum homogeneous spaces, duality and quantum 2-spheres (1994)
    Springer
    Geometriae dedicata 52 (1994), S. 291-315 
    Details
    ISSN: 1572-9168
    Keywords: 16W30 ; 17B37 ; 22E99 ; quantum groups ; quantum homogeneous spaces ; coaction ; dual Hopf algebras ; two-sided coideals ; infinitesimal invariance ; quantum SU(2) ; sl(2) quantized universal enveloping algebra ; quantum 2-spheres
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a quantum groupG the notion of quantum homogeneousG-space is defined. Two methods to construct such spaces are discussed. The first one makes use of quantum subgroups, the second more general one is based upon the notion of infinitesimal invariance with respect to certain two-sided coideals in the Hopf algebra dual to the Hopf algebra ofG. These methods are applied to the quantum group SU(2). As two-sided coideals we take the subspaces spanned by twisted primitive elements in the sl(2) quantized universal enveloping algebra. A one-parameter series of mutually non-isomorphic quantum 2-spheres is obtained, together with the spectral decomposition of the corresponding right regular representation of quantum SU(2). The link with the quantum spheres defined by Podleś is established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01278478
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  • 9
    Electronic Resource
    Electronic Resource
    An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds (1990)
    Springer
    Mathematical programming 46 (1990), S. 321-328 
    Details
    ISSN: 1436-4646
    Keywords: Global optimization ; separable programming ; quadratic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper gives an O(n) algorithm for a singly constrained convex quadratic program using binary search to solve the Kuhn-Tucker system. Computational results indicate that a randomized version of this algorithm runs in expected linear time and is suitable for practical applications. For the nonconvex case anε-approximate algorithm is proposed which is based on convex and piecewise linear approximations of the objective function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585748
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  • 10
    Electronic Resource
    Electronic Resource
    An algorithm for solving convex programs with an additional convex—concave constraint (1993)
    Springer
    Mathematical programming 61 (1993), S. 75-87 
    Details
    ISSN: 1436-4646
    Keywords: Global optimization ; branch-and-bound ; convex—concave constraint ; d.c. programming ; the product of two affine functions ; decomposition method ; algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An implementable decomposition method based on branch-and-bound techniques is proposed for finding a global optimal solution of certain convex programs with an additional convex—concave constrainth(x, y) ⩽ 0. A nonadaptive simplicial and an adaptive bisection are used for the branching operation, which is performed iny-space only. The bounding operation is based on a relaxation of the convex—concave constrainth(x, y) ⩽ 0. The algorithm can be applied efficiently for linear programs with an additional affine multiplicative constraint.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582140
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