Dear list members,

I have recently become interested in interval methods = as a means of solving non-linear non-convex optimisation problems and I = am looking to employ them in my own fields of work (traffic and = transport engineering and econometrics).

However, part of the problems I'd like to work on with = intervals are actually integer programs and I do not have, so far, a = clear grasp of how applicable are interval methods in this = case.

Could you point me to papers, books sections or other = resources discussing the applications of interval methods to the = solution of (non-linear) integer programs?

Many thanks

Dr Andrea Rosa

SBE - Napier University

Edinburgh, UK

tel ++44 (0) 131 455 2223

fax ++44 (0) 131 455 2239

I cannot point you to references, but I can offer that one approach I suppo= se is considered well known in the community is to apply interval methods to= the continuous problem. When the interval of real numbers contains on= ly one integer, snap to that integer. You sort of run a continuous alg= orithm with a tolerance of 0.99.

Others may have more directly applicable references.

Dr. George F. Corliss

Electrical and Computer Engineering

Marquette University

PO Box 1881

1515 W. Wisconsin Ave.

Milwaukee WI 53201-1881 USA

414-288-6599; Fax: 288-5579; Dept. 288-6280

George.Corliss [at] Marquette [dot] edu

Dear list members,

I have recently become interested in interval methods as a means of solving= non-linear non-convex optimisation problems and I am looking to employ them= in my own fields of work (traffic and transport engineering and econometric= s).

However, part of the problems I'd like to work on with intervals are actual= ly integer programs and I do not have, so far, a clear grasp of how applicab= le are interval methods in this case.

Could you point me to papers, books sections or other resources discussing = the applications of interval methods to the solution of (non-linear) integer= programs?

Many thanks

Dr Andrea Rosa

SBE - Napier University

Edinburgh, UK

tel ++44 (0) 131 455 2223

fax ++44 (0) 131 455 2239

--B_3177554424_169087-- From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Sep 9 07:22:20 2004 Received: from interval.louisiana.edu (localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id i89CMK3Q009670 for

When the variables xi must be integers, Hansen proposes (in "Global =
Optimization Using Interval Analysis", pg 214) to solve a constrained =
problem by=20
adding constraints like

sin (pi*xi)=3D0

Claudio Rocco

------=_NextPart_000_001D_01C4968A.14516B70-- From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Sep 9 16:51:08 2004 Received: from interval.louisiana.edu (localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id i89Lp8Ye010461 for----- Original Message -----From:=20 Rosa,=20 AndreaSent:Thursday, September 09, = 2004 6:28=20 AMSubject:intervals for integer=20 programsDear list members,

I have recently become interested in interval = methods as a=20 means of solving non-linear non-convex optimisation problems and I am = looking=20 to employ them in my own fields of work (traffic and transport = engineering and=20 econometrics).

However, part of the problems I'd like to work on = with=20 intervals are actually integer programs and I do not have, so far, a = clear=20 grasp of how applicable are interval methods in this case.

Could you point me to papers, books sections or = other=20 resources discussing the applications of interval methods to the = solution of=20 (non-linear) integer programs?

Many thanks

Dr Andrea Rosa

SBE - = Napier=20 University

Edinburgh, UK

tel ++44 (0) 131 455 2223

fax = ++44 (0)=20 131 455 2239

Dear Colleagues,

My address and the address of Reliable =
Computing=20
journal changed.

The former address was slnest [at] comset [dot] net.

The old address will be functional for =
some time=20
but please use the new one.

Sorry for inconvenience.

Best regards,

Slava

------=_NextPart_000_00C8_01C49714.465B38A0--
From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Sep 10 11:36:33 2004
Received: from interval.louisiana.edu (localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id i8AGaXvB012357
for Dear=20
all,

just to =
answer to=20
the message from Martin Berz : I do not have a test problem as =
yet. I actually wrote to the list since I am at a preliminary =
stage=20
(thinking of a project and surveying interesting methods) and aware of =
part of=20
the literature on interval methods but also looking for =
further=20
relevant references. I had read the section on integers in =
Hansen's book=20
but I was wondering whether there were further publications and, also, =
published=20
work on practical experiences.

So I guess =
the way the=20
discussion has developed, referring to (mixed) integer programming in =
general,=20
is the kind of response I was hoping to read (and, by the way, many =
thanks to=20
all those who posted contributions).

Andrea=20
Rosa

------_=_NextPart_001_01C4997B.E47BF223--
From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Sep 13 06:54:15 2004
Received: from interval.louisiana.edu (localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id i8DBsELm019460
for Dear=20
Andrea et al.,

very=20
well. Considering how attractive many of the fundamental =
properties of=20
validated methods are, there is sometimes a tendency to lose sight of =
the=20
connection to the practical problem at hand, and get absorbed by the =
appealing=20
and often challenging algorithmic questions. I have observed it often =
myself,=20
and found it important to always try to remind me what the specific =
question to be solved was; at least that's what my funding=20
agencies always seem to be concerned=20
about :-)

In any=20
case, please enjoy the discussion, let's hope we all =
learn=20
something from it, and it will lead to viable tools for the problems you =
may=20
wish to solve. And once you have more specific ideas what test or real =
problems=20
you are interested in, at least I personally would be interested in=20
them.

Best=20
wishes,

Martin

-----Original Message-----From:=20 owner-reliable_computing [at] interval [dot] louisiana.edu=20 [mailto:owner-reliable_computing [at] interval [dot] louisiana.edu]On Behalf = Of=20Rosa, AndreaSent:Monday, September 13, 2004 6:25=20 AMTo:= reliable_computing [at] interval [dot] louisiana.eduSubject:=20 RE: intervals for integer programs

Dear all,

just to answer to the message from Martin = Berz :=20 I do not have a test problem as yet. I actually wrote to = the list=20 since I am at a preliminary stage (thinking of a project and = surveying=20 interesting methods) and aware of part of the literature on interval = methods=20 but also looking for further relevant references. I = had read=20 the section on integers in Hansen's book but I was wondering whether = there=20 were further publications and, also, published work on practical=20 experiences.

So I guess the way the discussion has developed, = referring to=20 (mixed) integer programming in general, is the kind of response I was = hoping=20 to read (and, by the way, many thanks to all those who posted=20 contributions).

Andrea=20 Rosa

&nbs=
p; =20
Reliable=20
Computing

= =20 Volume 11, issue 1, 2005

= =20 Volume 11, issue 1, 2005

&nbs=
p;=20
Mathematical Research

Contracting Optimally an Interval =
Matrix =20
without

Loosing Any Positive Semi-Definite Matrix Is a Tractable=20 Problem

Luc Jaulin, Didier Henrion

1-17

Loosing Any Positive Semi-Definite Matrix Is a Tractable=20 Problem

Luc Jaulin, Didier Henrion

1-17

Computing System Reliability =
Given=20
Interval-Valued Characteristics of

the Components

Lev V. = Utkin, Igor=20 O. Kozine

19-34

the Components

Lev V. = Utkin, Igor=20 O. Kozine

19-34

A Normal Form Supplement to the =
Oettli-Prager=20
Theorem

Jiri Rohn

35-39

Jiri Rohn

35-39

Interval Schemes for Singularly =
Perturbed =20
Initial Value Problems

Abdelhay A. Salama, Emad = Hamdy

41-58

Abdelhay A. Salama, Emad = Hamdy

41-58

Outlier Detection under Interval=20
Uncertainty:

Algorithmic Solvability and Computational = Complexity

Vladik=20 Kreinovich, Luc Longpre, Praveen Patangay,

Scott Ferson, Lev=20 Ginzburg

59-76

Algorithmic Solvability and Computational = Complexity

Vladik=20 Kreinovich, Luc Longpre, Praveen Patangay,

Scott Ferson, Lev=20 Ginzburg

59-76

On the Proofs of Some Statements = Concerning the=20 Theorems

of Kantorovich, Moore, and Miranda

Marco = Schnurr

77-85