Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1573-2878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 2
    ISSN: 1573-2878
    Keywords: multiple-objective linear programming ; vector maximization ; efficient points ; weight set
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Approaches for generating the set of efficient extreme points of the decision set of a multiple-objective linear program (P) that are based upon decompositions of the weight set W0 suffer from one of two special drawbacks. Either the required computations are redundant, or not all of the efficient extreme point set is found. This article shows that the weight set for problem (P) can be decomposed into a partition based upon the outcome set Y of the problem, where the elements of the partition are in one-to-one correspondence with the efficient extreme points of Y. As a result, the drawbacks of the decompositions of W0 based upon the decision set of problem (P) disappear. The article explains also how this new partition offers the potential to construct algorithms for solving large-scale applications of problem (P) in the outcome space, rather than in the decision space.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 3
    ISSN: 1573-2878
    Keywords: unconstrained optimization ; Newton method ; Choleski factorization ; preconditioned conjugate gradient iteration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We propose a local algorithm for smooth unconstrained optimization problems with n variables. The algorithm is the optimal combination of an exact Newton step with Choleski factorization and several inexact Newton steps with preconditioned conjugate gradient subiterations. The preconditioner is taken as the inverse of the Choleski factorization in the previous exact Newton step. While the Newton method is converging precisely with Q-order 2, this algorithm is also precisely converging with Q-order 2. Theoretically, its average number of arithmetic operations per step is much less than the corresponding number of the Newton method for middle-scale and large-scale problems. For instance, when n=200, the ratio of these two numbers is less than 0.53. Furthermore, the ratio tends to zero approximately at a rate of log 2/logn when n approaches infinity.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 4
    ISSN: 1573-2878
    Keywords: preorders ; maximal points ; efficient points ; existence results
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Existence results of maximal points with respect to general binary relations were stated by Hazen and Morin (Ref. 1) and by Gajek and Zagrodny (Ref. 2). In this paper, we point out that the natural framework for this problem is that of transitive and reflexive relations (preorders). The aim of this paper is to discuss existence results for maximal points with respect to general transitive relations in such a way that, when considering them for preorders defined by convex cones, we are able to recover most known existence results for efficient points; the quasi-totality of them, with their (short) proofs, is presented, too.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 5
    ISSN: 1573-2878
    Keywords: nonlinear complementarity problems ; exceptional family of elements ; quasi-P*-maps ; P(τ, α, β)-maps ; exceptional regularity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Quasi-P*-maps and P(τ, α, β)-maps defined in this paper are two large classes of nonlinear mappings which are broad enough to include P*-maps as special cases. It is of interest that the class of quasi-P*-maps also encompasses quasimonotone maps (in particular, pseudomonotone maps) as special cases. Under a strict feasibility condition, it is shown that the nonlinear complementarity problem has a solution if the function is a nonlinear quasi-P*-map or P(τ, α, β)-map. This result generalizes a classical Karamardian existence theorem and a recent result concerning quasimonotone maps established by Hadjisawas and Schaible, but restricted to complementarity problems. A new existence result under an exceptional regularity condition is also established. Our method is based on the concept of exceptional family of elements for a continuous function, which is a powerful tool for investigating the solvability of complementarity problems.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 6
    ISSN: 1573-2878
    Keywords: generalized KKM mappings ; transfer closed-valued mappings ; γ-transfer lower semi-continuous functions ; minimax inequalities ; generalized variational inequalities ; generalized quasi-variational inequalities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, a general version of the KKM theorem is derived by using the concept of generalized KKM mappings introduced by Chang and Zhang. By employing our general KKM theorem, we obtain a general minimax inequality which contains several existing ones as special cases. As applications of our general minimax inequality, we derive an existence result for saddle-point problems under general setting. We also establish several existence results for generalized variation inequalities and generalized quasi-variational inequalities.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 7
    ISSN: 1573-2878
    Keywords: mathematical programming ; interior-point methods ; inexact Newton methods ; global convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Interior-point methods have been developed largely for nonlinear programming problems. In this paper, we generalize the global Newton interior-point method introduced in Ref. 1 and we establish a global convergence theory for it, under the same assumptions as those stated in Ref. 1. The generalized algorithm gives the possibility of choosing different descent directions for a merit function so that difficulties due to small steplength for the perturbed Newton direction can be avoided. The particular choice of the perturbation enables us to interpret the generalized method as an inexact Newton method. Also, we suggest a more general criterion for backtracking, which is useful when the perturbed Newton system is not solved exactly. We include numerical experimentation on discrete optimal control problems.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 8
    ISSN: 1573-2878
    Keywords: Nonconvex optimization ; Lagrangian function ; local convexification ; local duality ; p-power formulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is well-known that a basic requirement for the development of local duality theory in nonconvex optimization is the local convexity of the Lagrangian function. This paper shows how to locally convexify the Lagrangian function and thus expand the class of optimization problems to which dual methods can be applied. Specifically, we prove that, under mild assumptions, the Hessian of the Lagrangian in some transformed equivalent problem formulations becomes positive definite in a neighborhood of a local optimal point of the original problem.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 9
    ISSN: 1573-2878
    Keywords: Singular perturbations ; self-adjoint boundary-value problems ; asymptotic approximations ; boundary layers ; finite-difference schemes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A numerical method for singularly-perturbed self-adjoint boundary-value problems for second-order ordinary differential equations subject to Neumann boundary conditions is proposed. In this method (booster method), an asymptotic approximation is incorporated into a finite-difference scheme to improve the numerical solution. Uniform error estimates are derived for this method when implemented in known difference schemes. Numerical examples are presented to illustrate the present method.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 10
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1573-2878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...