Что (кто) такое well-ordered sets - определение

SPECIAL CASE OF DISCRETE OPTIMIZATION

Special Ordered Sets

well-ordered set

TOTAL ORDER SUCH THAT EVERY NONEMPTY SUBSET OF THE DOMAIN HAS A LEAST ELEMENT

Well-ordered set; Well-ordered; Well-ordering; Well ordered; Well ordering; Well-ordering property; Wellorder; Wellordering; Well ordered set; Wellordered; Well ordering theory; Well ordering property; Well-Ordering; Well-Ordered; Well-orderable set; Well order

<mathematics> A set with a total ordering and no infinite descending chains. A total ordering "<=" satisfies x <= x x <= y <= z => x <= z x <= y <= x => x = y for all x, y: x <= y or y <= x In addition, if a set W is well-ordered then all non-empty subsets A of W have a least element, i.e. there exists x in A such that for all y in A, x <= y. Ordinals are isomorphism classes of well-ordered sets, just as integers are isomorphism classes of finite sets. (1995-04-19)

Well-quasi-ordering

$'''Pic.3:''' Hasse diagram of <math>\N^2</math> with componentwise order$

PREORDER IN WHICH EVERY INFINITE SEQUENCE HAS AN INCREASING OR EQUIVALENT PAIR OF CONSECUTIVE VALUES

Well partial order; WQO; Well quasi ordering; Wellquasiorder; Well-quasi-order; Well quasi order; Wqo; Well-quasi order; Well-partial-order

In mathematics, specifically order theory, a well-quasi-ordering or wqo is a quasi-ordering such that any infinite sequence of elements x_0, x_1, x_2, \ldots from X contains an increasing pair x_i\le x_j with i.

https://en.wikipedia.org/wiki/Well-quasi-ordering

All's Well That Ends Well

PLAY BY SHAKESPEARE

All's Well that Ends Well; All's well that ends well; Capilet; Parolles; All's well that ends well (proverb); Alls Well That Ends Well; All's Well That End's Well; All's Well, that Ends Well

All's Well That Ends Well is a play by William Shakespeare, published in the First Folio in 1623, where it is listed among the comedies. There is a debate regarding the dating of the composition of the play, with possible dates ranging from 1598 to 1608.

https://en.wikipedia.org/wiki/All's_Well_That_Ends_Well

Википедия

Special ordered set

In discrete optimization, a special ordered set (SOS) is an ordered set of variables used as an additional way to specify integrality conditions in an optimization model. Special order sets are basically a device or tool used in branch and bound methods for branching on sets of variables, rather than individual variables, as in ordinary mixed integer programming. Knowing that a variable is part of a set and that it is ordered gives the branch and bound algorithm a more intelligent way to face the optimization problem, helping to speed up the search procedure. The members of a special ordered set individually may be continuous or discrete variables in any combination. However, even when all the members are themselves continuous, a model containing one or more special ordered sets becomes a discrete optimization problem requiring a mixed integer optimizer for its solution.

The ‘only’ benefit of using Special Ordered Sets compared with using only constraints is that the search procedure will generally be noticeably faster. As per J.A. Tomlin, Special Order Sets provide a powerful means of modeling nonconvex functions and discrete requirements, though there has been a tendency to think of them only in terms of multiple-choice zero-one programming.

https://en.wikipedia.org/wiki/Special ordered set