LGO
An Integrated Solver Suite
for Continuous Global and Local Optimization
(C) János D. Pintér
Pintér Consulting Services, Inc. (PCS) and Dalhousie
University
PCS address: 129 Glenforest Drive, Halifax, NS, Canada B3M 1J2
Phone:
1-(902)-443-5910
E-mail: jdpinter@hfx.eastlink.ca
URL:
http://www.dal.ca/~jdpinter
http://www.pinterconsulting.com
Summary
A large variety of decision issues in the applied sciences, engineering,
economics and finances can be modelled as constrained optimization problems.
The objective of
global optimization (GO) is to find the best solution of nonlinear decision
models, in the - possible or verified - presence of multiple local solutions.
The LGO program system solves (Lipschitz-)continuous global optimization
problems on finite 'box' regions, in the possible presence of additional
(Lipschitz-)continuous constraints. These mild structural assumptions
make possible the application of LGO under very general conditions.
LGO Solver Suite
The current LGO implementations incorporate the following solver modules that
can be selected by the user:
- Branch-and-bound global search method (BB)
- Global adaptive random search (GARS)
- Multi-start based global random search (MS)
- Constrained local search (LS) based on the reduced gradient method
Each selected global solver mode is automatically followed by the local solver.
This modular structure supports LGO's usage as a global solver, and also as a
general purpose (dense nonlinear) local solver.
Implementation Platforms
The LGO program system has been implemented on personal computer and workstation platforms,
across a variety of modeling environments. These currently include the following:
- LGO solver suite for global and local optimization, with a text I/O interface
(for C/C++ and Fortran compiler platforms); distributed by Pintér Consulting Services, Inc.
Contact us.
- LGO solver suite with a Microsoft Windows interface (LGO IDE; for Visual Basic,
C/C++, Delphi, and Fortran compiler platforms); distributed by PCS.
Contact us.
- LGO solver engine for Excel users;
distributed by Frontline Systems, Inc.
- LGO solver engine for GAMS users;
distributed by the GAMS Development Corporation
- LGO solver engine for MATLAB users; distributed by PCS
contact us,
and by
TOMLAB Optimization AB
- MathOptimizer Professional (LGO solver engine) for Mathematica users; distributed
by PCS
contact us,
and by
Wolfram Research, Inc.
An additional, but different solver implementation is
- MathOptimizer (native Mathematica) solver engine for Mathematica users;
distributed by PCS
contact us,
and by
Wolfram Research, Inc.
- Maple Global Optimization Toolbox (LGO solver engine) for Maple users; distributed by
Maplesoft, Inc.
All products are accompanied by a corresponding User's Guide, and benefit from technical support.
Professional (commercial), non-profit research and educational licenses are available:
please contact us
or our partners for current details and pricing.
Tutorials, workshops, and consulting services are offered.
We are also interested in joint model/application development projects.
Please contact us
for additional information.
Applications
For over 15 years (as of 2004), LGO has been applied to solve global optimization
problems (currently, in up to a few thousand decision variables and
constraints). LGO has been in use by leading universities, research institutions,
advanced industries and consulting companies in about 20 countries.
The extensive list of existing and potential LGO application areas includes,
for instance, the following broad problem-classes:
- advanced engineering design (acoustics, robotics, etc.)
- calibration of (laboratory, medical, etc.) instruments
- configuration design (e.g., in physical or chemical conformation modelling)
- data classification (cluster analysis)
- data visualization (e.g., multidimensional scaling) and state space reduction
- environmental engineering
- financial modeling and consulting
- general nonlinear approximation (including, e.g., various interpolation problems)
- model fitting to empirical data (identification, calibration and verification)
- optimized design and operation of 'black box' (confidential or other 'closed')
systems
- radiation therapy
- risk analysis and management, and other (potentially nonconvex) stochastic
decision problems
- robust product/mixture design (e.g., in chemical and processing industries)
- systems of nonlinear equations and inequalities
For additional information, please consult the illustrative list of
references provided at our websites, and
contact us.
Need more information?
Please visit
http://www.dal.ca/~jdpinter
http://www.pinterconsulting.com
and/or contact us.
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