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  • 1
    Electronic Resource
    Electronic Resource
    Genewindow: an interactive tool for visualization of genomic variation (2005)
    [s.l.] : Nature Publishing Group
    Nature genetics 37 (2005), S. 109-110 
    Details
    ISSN: 1546-1718
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Medicine
    Notes: [Auszug] To the editor: To facilitate the visualization of genetic variation in the context of the human genome, we developed a tool that permits 'gene-centric' annotation of the human genome for laboratory and analytical work carried out at the Core Genotyping Facility (CGF) of the National Cancer ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/ng0205-109
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  • 2
    Electronic Resource
    Electronic Resource
    A smoothing method for mathematical programs with equilibrium constraints (1999)
    Springer
    Mathematical programming 85 (1999), S. 107-134 
    Details
    ISSN: 1436-4646
    Keywords: Key words: equilibrium constraints – variational inequality problems – strong monotonicity – optimality conditions – global convergence ; Mathematics Subject Classification (1991): 90C30, 90C33, 65K05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s10107990015a
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  • 3
    Electronic Resource
    Electronic Resource
    An interior point algorithm of $$O(\sqrt m \left| {\ln \varepsilon } \right|)$$ iterations forC 1-convex programming (1992)
    Springer
    Mathematical programming 57 (1992), S. 239-257 
    Details
    ISSN: 1436-4646
    Keywords: Complexity of algorithms ; convergence analysis ; interior point algorithms ; Newton's methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a theoretical result on a path-following algorithm for convex programs. The algorithm employs a nonsmooth Newton subroutine. It starts from a near center of a restricted constraint set, performs a partial nonsmooth Newton step in each iteration, and converges to a point whose cost is withinε accuracy of the optimal cost in $$O(\sqrt m \left| {\ln \varepsilon } \right|)$$ iterations, wherem is the number of constraints in the problem. Unlike other interior point methods, the analyzed algorithm only requires a first-order Lipschitzian condition and a generalized Hessian similarity condition on the objective and constraint functions. Therefore, our result indicates the theoretical feasibility of applying interior point methods to certainC 1-optimization problems instead ofC 2-problems. Since the complexity bound is unchanged compared with similar algorithms forC 2-convex programming, the result shows that the smoothness of functions may not be a factor affecting the complexity of interior point methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581083
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  • 4
    Electronic Resource
    Electronic Resource
    A trust region algorithm for minimization of locally Lipschitzian functions (1994)
    Springer
    Mathematical programming 66 (1994), S. 25-43 
    Details
    ISSN: 1436-4646
    Keywords: Trust region methods ; Locally Lipschitzian functions ; Global convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The classical trust region algorithm for smooth nonlinear programs is extended to the nonsmooth case where the objective function is only locally Lipschitzian. At each iteration, an objective function that carries both first and second order information is minimized over a trust region. The term that carries the first order information is an iteration function that may not explicitly depend on subgradients or directional derivatives. We prove that the algorithm is globally convergent. This convergence result extends the result of Powell for minimization of smooth functions, the result of Yuan for minimization of composite convex functions, and the result of Dennis, Li and Tapia for minimization of regular functions. In addition, compared with the recent model of Pang, Han and Rangaraj for minimization of locally Lipschitzian functions using a line search, this algorithm has the same convergence property without assuming positive definiteness and uniform boundedness of the second order term. Applications of the algorithm to various nonsmooth optimization problems are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581136
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  • 5
    Electronic Resource
    Electronic Resource
    Continuous approximation schemes for stochastic programs (1995)
    Springer
    Annals of operations research 56 (1995), S. 15-38 
    Details
    ISSN: 1572-9338
    Keywords: Approximation ; derivative ; continuous distribution ; stochastic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract One of the main methods for solving stochastic programs is approximation by discretizing the probability distribution. However, discretization may lose differentiability of expectational functionals. The complexity of discrete approximation schemes also increases exponentially as the dimension of the random vector increases. On the other hand, stochastic methods can solve stochastic programs with larger dimensions but their convergence is in the sense of probability one. In this paper, we study the differentiability property of stochastic two-stage programs and discuss continuous approximation methods for stochastic programs. We present several ways to calculate and estimate this derivative. We then design several continuous approximation schemes and study their convergence behavior and implementation. The methods include several types of truncation approximation, lower dimensional approximation and limited basis approximation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02031698
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  • 6
    Electronic Resource
    Electronic Resource
    An SQP algorithm for extended linear-quadratic problems in stochastic programming (1995)
    Springer
    Annals of operations research 56 (1995), S. 251-285 
    Details
    ISSN: 1572-9338
    Keywords: Stochastic programming ; quadratic programming ; convergence ; B-regularity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Extended Linear-Quadratic Programming (ELQP) problems were introduced by Rockafellar and Wets for various models in stochastic programming and multistage optimization. Several numerical methods with linear convergence rates have been developed for solving fully quadratic ELQP problems, where the primal and dual coefficient matrices are positive definite. We present a two-stage sequential quadratic programming (SQP) method for solving ELQP problems arising in stochastic programming. The first stage algorithm realizes global convergence and the second stage algorithm realizes superlinear local convergence under a condition calledB-regularity.B-regularity is milder than the fully quadratic condition; the primal coefficient matrix need not be positive definite. Numerical tests are given to demonstrate the efficiency of the algorithm. Solution properties of the ELQP problem underB-regularity are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02031711
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  • 7
    Electronic Resource
    Electronic Resource
    Secant methods for semismooth equations (1998)
    Springer
    Numerische Mathematik 80 (1998), S. 305-324 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. Some generalizations of the secant method to semismooth equations are presented. In the one-dimensional case the superlinear convergence of the classical secant method for general semismooth equations is proved. Moreover a new quadratically convergent method is proposed that requires two function values per iteration. For the n-dimensional cases, we discuss secant methods for two classes of composite semismooth equations. Most often studied semismooth equations are of such form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050369
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  • 8
    Electronic Resource
    Electronic Resource
    Directed submodularity, ditroids and directed submodular flows (1988)
    Springer
    Mathematical programming 42 (1988), S. 579-599 
    Details
    ISSN: 1436-4646
    Keywords: Submodularity ; directed subsets ; ditroids ; total dual integrality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Set relations and operations such as inclusion, union and intersection are generalized to directed subsets whose elements are distinguished between forward and backward elements. The concepts of submodular functions, matroids and polymatroidal network flows are extended to the concepts of directed submodular functions, ditroids and directed submodular flows on directed subsets. Two unrelated matroids (submodular functions) can be embedded in one ditroid (directed submodular function). Total dual integrality is preserved in these generalizations and proved for very general set-function class-directed odd submodular functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589420
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  • 9
    Electronic Resource
    Electronic Resource
    Quasidifferentials and maximal normal operators (1990)
    Springer
    Mathematical programming 49 (1990), S. 263-271 
    Details
    ISSN: 1436-4646
    Keywords: Subdifferential ; quasidifferential ; semicontinuous operator ; maximal normal operator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Quasidifferentials are studied with the theory of maximal normal operators. The quasidifferential of a normally quasidifferentiable function is a pair of upper and lower semicontinuous operators, which are special maximal normal operators. The function sum of the upper and lower semicontinuous operators is the Clarke subdifferential of this function. Basic calculus and minimal forms of quasidifferentials are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588791
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  • 10
    Electronic Resource
    Electronic Resource
    A nonsmooth version of Newton's method (1993)
    Springer
    Mathematical programming 58 (1993), S. 353-367 
    Details
    ISSN: 1436-4646
    Keywords: Newton's methods ; generalized Jacobian ; semismoothness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Newton's method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized Jacobian instead of the derivative. This extension includes the B-derivative version of Newton's method as a special case. Convergence theorems are proved under the condition of semismoothness. It is shown that the gradient function of the augmented Lagrangian forC 2-nonlinear programming is semismooth. Thus, the extended Newton's method can be used in the augmented Lagrangian method for solving nonlinear programs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581275
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