ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

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

Proceed reservation?

Export
Filter
  • Articles  (12)
  • 06A10  (7)
  • Unconstrained optimization  (5)
  • 2015-2019
  • 1980-1984  (12)
  • 1970-1974
  • 1950-1954
  • 1940-1944
  • 1984  (12)
  • Mathematics  (12)
Collection
  • Articles  (12)
Source
Keywords
Publisher
Years
  • 2015-2019
  • 1980-1984  (12)
  • 1970-1974
  • 1950-1954
  • 1940-1944
Year
Topic
  • 1
    Electronic Resource
    Electronic Resource
    Maximum antichains in the product of chains (1984)
    Springer
    Order 1 (1984), S. 21-28 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 05A05 ; Partially ordered sets ; Sperner's Theorem ; LYM property ; product of chains
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let P be the poset k 1 × ... × k n , which is a product of chains, where n≥1 and k 1≥ ... ≥k n ≥2. Let $$M = k_1 - \sum\nolimits_{i = 2}^n {(k_i - 1)} $$ . P is known to have the Sperner property, which means that its maximum ranks are maximum antichains. Here we prove that its maximum ranks are its only maximum antichains if and only if either n=1 or M≤1. This is a generalization of a classical result, Sperner's Theorem, which is the case k 1= ... =k n =2. We also determine the number and location of the maximum ranks of P.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00396270
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Finite cutsets and finite antichains (1984)
    Springer
    Order 1 (1984), S. 35-46 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; Ordered set ; chain ; antichains ; width ; cutset
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An ordered set (P,≤) has the m cutset property if for each x there is a set Fx with cardinality less than m, such that each element of Fx is incomparable to x and {x} ∪ Fx meets every maximal chain of (P,≤). Let n be least, such that each element x of any P having the m cutset property belongs to some maximal antichain of cardinality less than n. We specify n for m 〈 w. Indeed, n-1=m= width P for m=1,2,n=5 if m=3 and n⩾ℵ1 if m ≥4. With the added hypothesis that every bounded chain has a supremum and infimum in P, it is shown that for 4⩽m⩽ℵ0, n=ℵ0. That is, if each element x has a finite cutset Fx, each element belongs to a finite maximal antichain.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00396272
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Minimizing the jump number for partially ordered sets: A graph-theoretic approach (1984)
    Springer
    Order 1 (1984), S. 7-19 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 05C20 ; 68C25 ; Partial order ; linear extension ; jump number ; line digraph ; cyclomatic number ; spanning branching ; Eulerian digraph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The purpose of this paper is to present a graph-theoretic approach to the jump number problem for N-free posets which is based on the observation that the Hasse diagram of an N-free poset is a line digraph. Therefore, to every N-free poset P we can assign another digraph which is the root digraph of the Hasse diagram of P. Using this representation we show that the jump number of an N-free poset is equal to the cyclomatic number of its root digraph and can be found (without producing any linear extension) by an algorithm which tests if a given poset is N-free. Moreover, we demonstrate that there exists a correspondence between optimal linear extensions of an N-free poset and spanning branchings of its root digraph. We provide also another proof of the fact that optimal linear extensions of N-free posets are exactly greedy linear extensions. In conclusion, we discuss some possible generalizations of these results to arbitrary posets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00396269
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Powers of ordered sets (1984)
    Springer
    Order 1 (1984), S. 83-92 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; Ordered sets ; exponentiation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently there has been significant progress in the study of powers of ordered sets. Much of this work has concerned cancellation laws for powers and uses these two steps. First, logarithmic operators are introduced to transform cancellation problems for powers into questions involving direct product decompositions. Second, refinement theorems for direct product decompositions are brought to bear. Here we present two results with the aim of highlighting these steps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00396275
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Balancing poset extensions (1984)
    Springer
    Order 1 (1984), S. 113-126 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 68E05 ; Sorting ; comparison ; information theoretic bound ; linear extension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We show that any finite partially ordered setP (not a total order) contains a pair of elementsx andy such that the proportion of linear extensions ofP in whichx lies belowy is between 3/11 and 8/11. A consequence is that the information theoretic lower bound for sorting under partial information is tight up to a multiplicative constant. Precisely: ifX is a totally ordered set about which we are given some partial information, and ife(X) is the number of total orderings ofX compatible with this information, then it is possible to sortX using no more thanC log2 e (X) comparisons whereC is approximately 2.17.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00565647
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    Ordered sets with no chains of ideals of a given type (1984)
    Springer
    Order 1 (1984), S. 159-172 
    Details
    ISSN: 1572-9273
    Keywords: 06A05 ; 06A10 ; Ordered sets ; ideals ; better quasi-order
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study the possible order types of chains of ideals in an ordered set. Our main result is this. Given an indecomposable countable order type α, there is a finite listA 1 α , ...,A n α of ordered sets such that for every ordered setP the setJ(P) of ideals ofP, ordered by inclusion, contains a chain of type α if and only ifP contains a subset isomorphic to one of theA 1 #x03B1; , ...,A n α . The finiteness of the list relies on the notion of better quasi-ordering introduced by Nash-Williams and the properties of scattered chains obtained by Laver.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00565651
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    Compactness and subsets of ordered sets that meet all maximal chains (1984)
    Springer
    Order 1 (1984), S. 147-157 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 54D30 ; Maximal chain ; cutset ; chain complete ; antichain ; cofinal subset
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetP be a chain complete ordered set. By considering subsets which meet all maximal chains, we describe conditions which imply that the space of maximal chains ofP is compact. The symbolsP 1 andP 2 refer to two particular ordered sets considered below. It is shown that the space of maximal chains ℳ (P) is compact ifP satisfies any of the following conditions: (i)P contains no copy ofP 1 or its dual and all antichains inP are finite. (ii)P contains no properN and every element ofP belongs to a finite maximal antichain ofP. (iii)P contains no copy ofP 1 orP 2 and for everyx inP there is a finite subset ofP which is coinitial abovex. We also describe an example of an ordered set which is complete and densely ordered and in which no antichain meets every maximal chain.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00565650
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Local and global optimization by parallel algorithms for MIMD systems (1984)
    Springer
    Annals of operations research 1 (1984), S. 151-164 
    Details
    ISSN: 1572-9338
    Keywords: Unconstrained optimization ; parallel algorithms ; MIMD systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper describes an implementation on the Neptune system at Loughborough University of Sutti's parallel (MIMD) algorithm [1–3] and an analysis of its performance. Parallel asynchronous versions of Powell's method [6] and Price's algorithm [7] are proposed, designed for efficient implementation on MIMD systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01876145
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    Some investigations in a new algorithm for nonlinear optimization based on conic models of the objective function (1984)
    Springer
    Journal of optimization theory and applications 43 (1984), S. 1-21 
    Details
    ISSN: 1573-2878
    Keywords: Unconstrained optimization ; collinear scaling method ; conic models ; quasi-Newton algorithms ; numerical algorithms ; non-linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An appealing approach to the solution of nonlinear optimization problems based on conic models of the objective function has been recently introduced by Davidon. It leads to a broad class of algorithms which, in some sense, can be considered to generalize the existing quasi-Newton algorithms. One particular member of this class has been deeply examined by Sorensen, who has proved some interesting theoretical properties. A new interpretation of this algorithm is suggested in this paper from a more straightforward and somewhat familiar point of view. In addition, numerical experiments have been carried out to compare the Sorensen algorithm with a straightforward BFGS implementation of the classical quasi-Newton method with the final aim to assess the real merits and benefits of the new algorithm. Although some challenging test functions are used in computational experiments, the results are not particularly favorable to the new algorithm. As a matter of fact they do not exhibit any jump of quality, as it might be expected. Lastly, it is pointed out that a difficulty may affect the new method in situations in which it is necessary to exploit the special structure of large-scale problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934743
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Use of a nonquadratic model in a conjugate-gradient method of optimization with inexact line searches (1984)
    Springer
    Journal of optimization theory and applications 43 (1984), S. 357-370 
    Details
    ISSN: 1573-2878
    Keywords: Unconstrained optimization ; rational models ; conjugate directions ; inexact line searches
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An algorithm for unconstrained minimization is developed which uses a rational function model, rather than a quadratic, as a basis for conjugate directions. The algorithm is similar to one previously proposed by the authors, but inexact linear searches are investigated in the present paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934460
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 11
    Electronic Resource
    Electronic Resource
    A conjugate-direction method based on a nonquadratic model (1984)
    Springer
    Journal of optimization theory and applications 43 (1984), S. 371-381 
    Details
    ISSN: 1573-2878
    Keywords: Unconstrained optimization ; conjugate-direction methods ; numerical algorithms ; rational models ; quadratic models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A conjugate-gradient method for unconstrained optimization, which is based on a nonquadratic model, is proposed. The technique has the same properties as the Fletcher-Reeves algorithm when applied to a quadratic function. It is shown to be efficient when tried on general functions of different dimensionality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934461
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 12
    Electronic Resource
    Electronic Resource
    Secant relations versus positive definiteness in quasi-Newton methods (1984)
    Springer
    Journal of optimization theory and applications 44 (1984), S. 681-687 
    Details
    ISSN: 1573-2878
    Keywords: Unconstrained optimization ; quasi-Newton methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The effect of using a nonsymmetric and nonpositive-definite matrix for approximation of the Hessian inverse in unconstrained optimization is investigated. To this end, a new algorithm, which may be viewed as a member of the Huang family, is derived. The proposed algorithm possesses the quadratic termination property without exact line search. It seems from the numerical results that it is not essential to use a symmetric and positive-definite matrix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938401
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...