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  • 1
    Digitale Medien
    Digitale Medien
    Optimizing over the subtour polytope of the travelling salesman problem (1990)
    Springer
    Mathematical programming 49 (1990), S. 163-187 
    Details
    ISSN: 1436-4646
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract A commonly studied relaxation of the travelling salesman problem is obtained by adding subtour elimination constraints to the constraints of a 2-factor problem and removing the integrality requirement. We investigate the problem of solving this relaxation for a special type of objective function. We also discuss some ways in which this relates to the concept of rank introduced by Chvátal.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01588786
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  • 2
    Digitale Medien
    Digitale Medien
    Concurrent stochastic methods for global optimization (1990)
    Springer
    Mathematical programming 46 (1990), S. 1-29 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Global optimization ; concurrent ; parallel ; stochastic ; network of computers
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585724
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  • 3
    Digitale Medien
    Digitale Medien
    Proximity control in bundle methods for convex nondifferentiable minimization (1990)
    Springer
    Mathematical programming 46 (1990), S. 105-122 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Nondifferentiable minimization ; convex programming ; numerical methods ; descent methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Proximal bundle methods for minimizing a convex functionf generate a sequence {x k } by takingx k+1 to be the minimizer of $$\hat f^k (x) + u^k |x - x^k |^2 /2$$ , where $$\hat f^k $$ is a sufficiently accurate polyhedral approximation tof andu k 〉 0. The usual choice ofu k = 1 may yield very slow convergence. A technique is given for choosing {u k } adaptively that eliminates sensitivity to objective scaling. Some encouraging numerical experience is reported.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585731
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  • 4
    Digitale Medien
    Digitale Medien
    Relaxation methods for monotropic programs (1990)
    Springer
    Mathematical programming 46 (1990), S. 127-151 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Dual descent ; monotropic program ; Tucker tableau ; elementary vector
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We propose a dual descent method for the problem of minimizing a convex, possibly nondifferentiable, separable cost subject to linear constraints. The method has properties reminiscent of the Gauss-Seidel method in numerical analysis and uses theε-complementary slackness mechanism introduced in Bertsekas, Hosein and Tseng (1987) to ensure finite convergence to near optimality. As special cases we obtain the methods in Bertsekas, Hosein and Tseng (1987) for network flow programs and the methods in Tseng and Bertsekas (1987) for linear programs.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585734
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  • 5
    Digitale Medien
    Digitale Medien
    Algebraic optimization: The Fermat-Weber location problem (1990)
    Springer
    Mathematical programming 46 (1990), S. 219-224 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Algebraic optimization ; location theory ; ellipsoid algorithms
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The Fermat-Weber location problem is to find a point in ℝ n that minimizes the sum of the (weighted) Euclidean distances fromm given points in ℝ n . In this work we discuss some relevant complexity and algorithmic issues. First, using Tarski's theory on solvability over real closed fields we argue that there is an infinite scheme to solve the problem, where the rate of convergence is equal to the rate of the best method to locate a real algebraic root of a one-dimensional polynomial. Secondly, we exhibit an explicit solution to the strong separation problem associated with the Fermat-Weber model. This separation result shows that anε-approximation solution can be constructed in polynomial time using the standard Ellipsoid Method.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585739
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  • 6
    Digitale Medien
    Digitale Medien
    A short proof of finiteness of Murty's principal pivoting algorithm (1990)
    Springer
    Mathematical programming 46 (1990), S. 255-256 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Linear complementarity problem ; P-matrix
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We give a short proof of the finiteness of Murty's principal pivoting algorithm for solving the linear complementarity problemy = Mz + q, y T z = 0,y ≥ 0,z ≥ 0 withP-matrixM.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585743
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  • 7
    Digitale Medien
    Digitale Medien
    Convergence properties of trust region methods for linear and convex constraints (1990)
    Springer
    Mathematical programming 47 (1990), S. 305-336 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Trust region ; linear constraints ; convex constraints ; global convergence ; local convergence ; degeneracy ; rate of convergence ; identification of active constraints ; Newton's method ; sequential quadratic programming ; gradient projection
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We develop a convergence theory for convex and linearly constrained trust region methods which only requires that the step between iterates produce a sufficient reduction in the trust region subproblem. Global convergence is established for general convex constraints while the local analysis is for linearly constrained problems. The main local result establishes that if the sequence converges to a nondegenerate stationary point then the active constraints at the solution are identified in a finite number of iterations. As a consequence of the identification properties, we develop rate of convergence results by assuming that the step is a truncated Newton method. Our development is mainly geometrical; this approach allows the development of a convergence theory without any linear independence assumptions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01580867
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  • 8
    Digitale Medien
    Digitale Medien
    Active set algorithms for isotonic regression; A unifying framework (1990)
    Springer
    Mathematical programming 47 (1990), S. 425-439 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Isotonic regression ; active sets
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this and subsequent papers we will show that several algorithms for the isotonic regression problem may be viewed as active set methods. The active set approach provides a unifying framework for studying algorithms for isotonic regression, simplifies the exposition of existing algorithms and leads to several new efficient algorithms. We also investigate the computational complexity of several algorithms. In this paper we consider the isotonic regression problem with respect to a complete order $$\begin{gathered} minimize\sum\limits_{i = 1}^n {w_i } (y_i - x_i )^2 \hfill \\ subject tox_1 \leqslant x_2 \leqslant \cdot \cdot \cdot \leqslant x_n \hfill \\ \end{gathered} $$ where eachw i is strictly positive and eachy i is an arbitrary real number. We show that the Pool Adjacent Violators algorithm (due to Ayer et al., 1955; Miles, 1959; Kruskal, 1964), is a dual feasible active set method and that the Minimum Lower Set algorithm (due to Brunk et al., 1957) is a primal feasible active set method of computational complexity O(n 2). We present a new O(n) primal feasible active set algorithm. Finally we discuss Van Eeden's method and show that it is of worst-case exponential time complexity.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01580873
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  • 9
    Digitale Medien
    Digitale Medien
    Call for nominations for the D.R. Fulkerson Prize 1991 (1990)
    Springer
    Mathematical programming 47 (1990), S. 463-463 
    Details
    ISSN: 1436-4646
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01580877
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  • 10
    Digitale Medien
    Digitale Medien
    On multilevel iterative methods for optimization problems (1990)
    Springer
    Mathematical programming 48 (1990), S. 1-17 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Coercivity ; quadratic programming ; linear programming ; aggregation ; relaxation ; multigrid methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper is concerned with multilevel iterative methods which combine a descent scheme with a hierarchy of auxiliary problems in lower dimensional subspaces. The construction of auxiliary problems as well as applications to elasto-plastic model and linear programming are described. The auxiliary problem for the dual of a perturbed linear program is interpreted as a dual of perturbed aggregated linear program. Coercivity of the objective function over the feasible set is sufficient for the boundedness of the iterates. Equivalents of this condition are presented in special cases.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01582249
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