Optimization
Contacts
J. Moré
Mihai Anitescu
S. Leyffer
T.S. Munson
Our optimization research has become a multipronged effort, including development of leading-edge methods and software, and exploration of network-based problem solving.
The Optimization Technology Center seeks to make potential users in industry, government, and academia aware of how optimization techniques can aid their work, and to make the latest techniques widely available over the Internet. Research focuses on developing new solvers (NEOS tools), new submission mechanisms (the NEOS Server), and an updated guide on optimization software (NEOS Guide). The NEOS products are designed to help at each stage of problem solving: modeling real-world applications, solving the mathematical problem, and interpreting the results.
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The MINPACK-2 project focuses on development of optimization algorithms and software for high-performance computers. As part of the MINPACK-2 project, we have developed a collection of test problems that are representative of interesting optimization problems arising in diverse applications.
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The
TAO
project focuses on the development of software for large-scale optimization problems on high-performance architectures.
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Towards Optimal Petascale Simulations (TOPS)
is a DOE-sponsored collaborative research effort by several universities and DOE laboratories under the SciDAC initiative. TOPS focuses on developing,
implementing, and supporting optimal or near-optimal schemes for PDE-based simulations and clostely related tasks.
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| Constrained nonlinear optimization
research is focusing on techniques to compute mountain passes -- critical
points where the Hessian has exactly one negative eigenvalue.
Mountain passes are of interest, for example, in computational chemistry,
where they correspond to transition states for chemical reacations.
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Mesh-quality optimization
research involves development of methods for improving tetrahedral meshes.
We consider such factors as problem size, element size, and heterogeneity
in comparing the effectiveness of inexact Newton and coordinate descent
optimization methods.
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Equilibrium problems with equilibrium constraints (EPECs)
arise in multileader-follower games when modeling competition between
two or more dominant firms. We are studying various nonlinear optimization and nonlinear complementarity formulations of EPECs.
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Mathematical programs with complementarity constraints (MPCCs)
are used to study optimal control of robot systems with friction.
The MPCC model is solved by using its elastic mode, a well-behaved nonlinear
programming problem.
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