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From: ylfink@water.UUCP (ylfink)
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Subject: UW Num. Optimization, Dr. Zheng on "Robust Analysis and its Applications".
Message-ID: <587@water.UUCP>
Date: Fri, 31-Oct-86 14:54:38 EST
Article-I.D.: water.587
Posted: Fri Oct 31 14:54:38 1986
Date-Received: Sat, 1-Nov-86 01:57:14 EST
Expires: Mon, 10-Nov-86 00:00:00 EST
Organization: U of Waterloo, Ontario
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DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF WATERLOO
SEMINAR ACTIVITIES

NUMERICAL OPTIMIZATION
(Joint with C&O)

                    - Friday, November 7, 1986.

Dr.  Quan  Zheng  of Shanghai University of Science and
Technology  will  speak  on  ``Robust  Analysis and its
Applications''.

TIME:                3:30 PM

ROOM:              MC 3003

ABSTRACT

Let  X  be  a topological space, and f be a real valued
function  on  X.   A subset G of X is said to be robust
iff  Cl(G)=Cl(f(G)).  A function f is said to be robust
iff  G sub c = {x | f(x)<c} is robust set for each real
number c.  Robust functions may be discontinuous.

It  is  easy to construct a discontinuous exact penalty
function  which can be used in constrained minimization
problems.    An  integer  programming  problem  can  be
thought  of as minimization of a discontinuous function
(each  function).  The maximum or minimum of a function
g(x,y)  with respect to variable y usually is a discon-
tinuous  function of x.  Under certain conditions it is
robust.   In this work we characterize the structure of
robust  sets  and robust functions, extend the integral
approach  of global optimization to the class of robust
functions and discuss the applications of these results
to the above mentioned problems.