Michael's Home Page: Nonlinear Programming Research
My interest in nonlinear programming algorithms grew out of my research in
transportation analysis. A common thread in my
research endeavours is a wish to not only contribute to scientific
knowledge, but also (and a wish that is equally strong) to place the existing
knowledge in a unified framework; this is, in my view, a far too overlooked
part of scientific research. My research has so far led to the formulation
and analysis of a general class of descent algorithms for nonlinear
programming problems, the class of cost approximation algorithms.
This class includes many classical algorithms, such as steepest descent and
Newton's algorithm in unconstrained optimization, the Frank-Wolfe and gradient
projection algorithms in differentiable, constrained optimization, and
regularization algorithms such as the proximal point algorithm for general
nondifferentiable optimization. The algorithm class has also been extended to
the solution of variational inequalities.
A second, and much more recent, interest, is in applications of mathematical
programming algorithms. Here you will find both reports related to the class of
cost approximation algorithms (including my PhD thesis) and recent applications
oriented ones. The latest addition (2005) is a report on a core problem, namely one
that often is referred to as the (continuous) nonlinear knapsack problem. "Not much
new is under the sun" is a rather good summary of this work.
Note: the preliminary reports may not be available yet.
Be patient; one of these days they will be ...
Text Books:
- Introduction to Continuous Optimization
(Studentlitteratur, 2005)
- Errata list for Introduction to
Continuous Optimization
- Order information for
Introduction to
Continuous Optimization
Monograph:
- Contents of
Nonlinear Programming and Variational Inequality Problems---A
Unified Approach
(Applied Optimization, Kluwer Academic Publishers, 1999):
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
Reports on Cost Approximation Concepts:
- Cost Approximation Algorithms (in
Encyclopedia of Optimization Floudas and Pardalos (eds.),
Kluwer Academic Publishers, 2001):
DVI or
PS format
- A Class of SQP Algorithms 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
- Cost Approximation Algorithms with Nonmonotone Line Searches for
a General Class of Nonlinear Programs
(Optimization, 44 (1998) 199-217):
DVI or
PS format;
ABSTRACT
- Cost Approximation: A Unified Framework of Descent
Algorithms For Nonlinear Programs
(SIAM Journal on Optimization, 8 (1998) 561-582):
DVI or
PS or
PDF format;
ABSTRACT
- Decomposition Methods For Differentiable Optimization Problems over
Cartesian Product Sets
(Computational Optimization and Applications, 9 (1998) 5-42):
DVI or
PS format;
ABSTRACT
- Parallel Cost Approximation Algorithms for Differentiable
Optimization
(In Parallel Computing in Optimization,
A. Migdalas, P. Pardalos and S. Storöy (eds.), Kluwer Academic
Publishers, New York, NY, 1997, pp. 295-341):
PS format;
ABSTRACT
- Partial Linearization Methods in Nonlinear Programming
(Journal of Optimization Theory and Applications,
78 (1993) 227-246):
DVI or
PS format;
ABSTRACT
Reports on Nondifferentiable Optimization:
- On the Convergence of Conditional
Epsilon-Subgradient Methods for Convex Programs and
Convex-Concave Saddle-Point Problems
[with Torbjörn Larsson and Ann-Brith Strömberg]
(European Journal of Operational Research, 151 (2003) 461-473):
DVI,
PDF,
PS format;
ABSTRACT
- Ergodic, Primal Convergence in Dual Subgradient Schemes for
Convex Programming
[with Torbjörn Larsson and Ann-Brith Strömberg]
(Mathematical Programming, 86 (1999) 283-312):
PS format;
PDF format;
ABSTRACT
- Ergodic Convergence in Subgradient Optimization
[with Torbjörn Larsson and Ann-Brith Strömberg]
(Optimization Methods and Software, 9 (1998) 93-120):
DVI or
PS format;
ABSTRACT
- Ergodic Results and Bounds on the Optimal Value in
Subgradient Optimization
[with Torbjörn Larsson and Ann-Brith Strömberg]
(In Operations Research Proceedings 1995,
Selected Papers of the Symposium on Operations Research (SOR '95),
Passau, September 13-15, 1995, P. Kleinschmidt, A. Bachem,
U. Derigs, D. Fischer, U. Leopold-Wildburger, and
R. Möhring (eds.), Springer-Verlag, Berlin, 1996,
pp. 30-35):
DVI or
PS format;
ABSTRACT
- Ergodic Results in Subgradient Optimization
[with Torbjörn Larsson and Ann-Brith Strömberg]
(In Nonlinear Optimization and Applications,
Proceedings of the International School of Mathematics
``G. Stampacchia'' 21st Workshop on Nonlinear Optimization and Applications,
held June 13-21, 1995, in Erice, Italy, G. Di Pillo and F. Giannessi
(eds.), Plenum Press, New York, NY, 1996, pp. 229-248):
DVI or
PS format;
ABSTRACT
- Conditional Subgradient Optimization-Theory and Applications
[with Torbjörn Larsson and Ann-Brith Strömberg]
( European Journal of Operational Research,
88 (1996) 382-403):
PS format;
ABSTRACT
Reports on Sensitivity Analysis:
- Sensitivity analysis of variational inequalities over
aggregated polyhedra, with application to traffic equilibria
[with R. Tyrrell Rockafellar]
(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
Reports on Stochastic Bilevel Programming:
- On the robustness of global optima and stationary solutions to
stochastic mathematical programs with equilibrium constraints, Part II:
Applications
[with Christoffer Cromvik]
(Journal of Optimization Theory and Applications 144 (2010) 479-500):
PDF
- On the robustness of global optima and stationary solutions to
stochastic mathematical programs with equilibrium constraints, Part I:
Theory
[with Christoffer Cromvik]
(Journal of Optimization Theory and Applications 144 (2010) 461-478):
PDF
- Stochastic Mathematical Programs With Equilibrium Constraints
[with Laura Wynter]
(Operations Research Letters 25 (1999) 159-167):
DVI or
PS format;
ABSTRACT
Reports on Engineering Applications:
- Combustion engine optimization: A multiobjective approach
[with S. Jakobsson, M. Saif-Ul-Hasnain, R. Rundqvist, F. Edelvik,
B. Andersson, M. Ljungqvist, D. Lortet, and J. Wallesten]
(in Optimization & Engineering, (2010, to appear))
DOI
- A method for simulation based optimization using
radial basis functions
[with S. Jakobsson, J. Rudholm, and A. Wojciechowsk]
(in Optimization & Engineering, (2010, to appear))
DOI
- On the Convergence of Stationary Sequences in Topology Optimization
[with A. Evgrafov]
(in International Journal of Numerical Methods in Engineering, 64 (2005)
17-44)
PDF format
- On the Existence of Solutions to Stochastic Mathematical Programs
with Equilibrium Constraints
[with A. Evgrafov]
(in Journal of Optimization Theory and Applications, 121 (2004) 65-76)
PDF format
- Stable Relaxations of Stochastic Stress Constrained Weight
Minimization Problems
[with A. Evgrafov]
(in Structural and Multidisciplinary Optimization, 25 (2003) 189-198)
PDF format
- Stochastic Structural Topology Optimization: Discretization and
Penalty Function Approach
[with A. Evgrafov]
(in Structural and Multidisciplinary Optimization, 25 (2003) 174-188)
PS format
- Stochastic Structural Topology Optimization: Existence of Solutions
and Sensitivity Analyses
[with A. Evgrafov and Joakim Petersson]
(in ZAMM, 83 (2003) 479-492):
PDF format
- On Stochastic Structural Topology Optimization
[with A. Evgrafov and J. Petersson]
(in Nonsmooth/Nonconvex Mechanics: With Applications in Engineering,
Proceedings of the International Conference in memory of Professor
P. D. Panagiotopoulos, 5-6 July 2002, Thessaloniki, Greece, C. C.
Baniotopoulos (ed.), Editions ZITI, Thessaloniki, Greece,
pp. 97-104):
PDF format
- Existence and Continuity of Optimal Solutions to some
Structural Topology Optimization Problems Including Unilateral
Constraints and Stochastic Loads
[with Joakim Petersson]
(ZAMM, 82 (2002) 435-459):
PS or
PDF
format;
ABSTRACT
- Stochastic Bilevel Programming in Structural Optimization
[with S. Christiansen and L. Wynter]
(Structural and Multidisciplinary Optimization, 21 (2001) 361-371):
PS or
PDF
format
- Topology Optimization of Sheets in Contact by a Subgradient
Method
[with Joakim Petersson]
(International Journal of Numerical Methods in
Engineering, 40 (1997) 1295-1321):
DVI or
PS format [PICTURES NOT INCLUDED!!];
ABSTRACT
- A Subgradient Method for Contact Structural Optimization
[with Joakim Petersson]
(In Complementarity and Variational Problems-State of the Art,
Proceedings of the International Conference on Complementarity
Problems (ICCP-95) held at The Johns Hopkins University,
Baltimore, MD, November 1995, Proceedings in Applied Mathematics,
vol. 92, M.C. Ferris and J.-S. Pang (eds.), SIAM, Philadelphia, PA, 1997,
pp. 295-314)
PS format
ABSTRACT
Reports on Column Generation Algorithms:
- Column Generation Algorithms for nonlinear optimization, II:
Numerical Investigations
[with Ricardo Garcia and Angel Marin]
(in Computers & Operations Research, 38 (2011) 591-604):
DOI
- A Class of Column Generation/Simplicial Decomposition in Convex
Differentiable Optimization, I: Convergence Analysis
[with Ricardo Garcia and Angel Marin]
(in Optimization, 52 (2003) 171-200):
DVI or
PS format;
ABSTRACT
- Simplicial Decomposition Algorithms (in Encyclopedia of
Optimization Floudas and Pardalos (eds.), Kluwer Academic
Publishers, 2001):
DVI or
PS format
- Simplicial Decomposition Algorithms with Nonlinear Column
Generation
[with Torbjörn Larsson and Clas Rydergren]
(under revision):
PS format;
ABSTRACT
- Applications of Simplicial Decomposition with Nonlinear Column
Generation to Nonlinear Network Flows
[with Torbjörn Larsson and Clas Rydergren]
(Network Optimization, Proceedings of the Network Optimization
Conference, University of Florida, Gainesville, FL, February 12-14, 1996,
P. Pardalos, W.W. Hager, and D.W. Hearn (eds.), Lecture Notes in
Economics and Mathematical Systems, vol. 450, Springer-Verlag, Berlin,
1997, pp. 346-373):
PS format;
ABSTRACT
- A Generic Column Generation Scheme
[with Torbjörn Larsson and Athanasios Migdalas]
(preliminary):
DVI or
PS format;
ABSTRACT
Reports on Resource Allocation Problems:
- A Survey on The Continuous Resource Allocation Problem
(European Journal of Operational Research 185 (2008) 1-46):
DVI,
PDF or
PS format;
ABSTRACT
Reports on Nonlinear Network Flow Problems:
