Michael's Home Page: Variational Inequality Problems Research
Variational inequalities constitute an important modelling tool, especially
for equilibrium type problems. My interest in this area arose when studying
problems in transportation analysis, which in
many cases can be formulated as variational inequality problems. My most
important contribution in the area is in the construction of descent
algorithms for the problem; these algorithms are all applications of the class
of cost approximation algorithms, which I originally formulated and analyzed
in the nonlinear programming setting.
Monograph:
- Contents of
Nonlinear Programming and Variational Inequality Problems---A
Unified Approach
(Applied Optimization, Kluwer Academic Publishers):
PS format
- Errata list for Nonlinear Programming and Variational
Inequality Problems---A Unified Approach (not included in
the printed version):
PS format
- Order information for
Nonlinear Programming and Variational Inequality Problems---A
Unified Approach
Dissertation:
- A Unified Framework of Descent
Algorithms For Nonlinear Programs and Variational Inequalities
(Department of Mathematics, Linköping University, September 1993):
PS format;
ABSTRACT
Reports:
- Sensitivity analysis of variational inequalities over
aggregated polyhedra, with application to traffic equilibria
[with R. Tyrrell Rockafellar]
(forthcoming in Equilibrium Problems and Variational Models,
Proceedings of the International School of Mathematics
``G. Stampacchia'' 32th Workshop, held June 23-July 2, 2000, in
Erice, Italy):
DVI or
PS format;
ABSTRACT
- A New Merit Function and an SQP Algorithm for Non-Strictly Monotone
Variational Inequalities (in Nonlinear
Optimization and Related Topics, Proceedings of the
International School of Mathematics ``G. Stampacchia'' 28th
Course on Nonlinear Optimization and Applications, held June
23-July 2, 1998, in Erice, Italy, G. Di Pillo and F. Giannessi
(eds.), Kluwer Academic Publishers, New York, NY, 1999, 257-275):
DVI or
PS format;
ABSTRACT
- A Taxonomy of Descent Algorithms For Nonlinear Programs
and Variational Inequalities
(revised ):
DVI or
PS format;
ABSTRACT
- Merit Functions and Descent Algorithm For a Class of Variational
Inequality Problems
(Optimization, 41 (1997) 37-55):
DVI or
PS format;
ABSTRACT
- On the Convergence of Descent Methods For Monotone Variational
Inequalities
(Operations Research Letters, 16 (1994) 265-269):
DVI or
PS format;
ABSTRACT
- A Class of Gap Functions For Variational Inequalities
[with Torbjörn Larsson]
(Mathematical Programming,
64 (1994) 53-79):
DVI or
PS format;
ABSTRACT
Michael Patriksson
Department of Mathematics,
Chalmers University of Technology,
Gothenburg (Göteborg)
mipat@math.chalmers.se