ylfink@water.UUCP (ylfink) (10/31/86)
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.