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AMPL: A Modeling Language for Mathematical Programming
Robert Fourer,Brian W. Kernighan +1 more
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TLDR
An efficient translator is implemented that takes as input a linear AMPL model and associated data, and produces output suitable for standard linear programming optimizers.Abstract:
Practical large-scale mathematical programming involves more than just the application of an algorithm to minimize or maximize an objective function. Before any optimizing routine can be invoked, considerable effort must be expended to formulate the underlying model and to generate the requisite computational data structures. AMPL is a new language designed to make these steps easier and less error-prone. AMPL closely resembles the symbolic algebraic notation that many modelers use to describe mathematical programs, yet it is regular and formal enough to be processed by a computer system; it is particularly notable for the generality of its syntax and for the variety of its indexing operations. We have implemented an efficient translator that takes as input a linear AMPL model and associated data, and produces output suitable for standard linear programming optimizers. Both the language and the translator admit straightforward extensions to more general mathematical programs that incorporate nonlinear expressions or discrete variables.read more
Citations
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Valid inequalities and restrictions for stochastic programming problems with first order stochastic dominance constraints
Nilay Noyan,Andrzej Ruszczyński +1 more
TL;DR: This paper considers a mixed 0–1 linear programming formulation of a discrete first order constrained optimization model and presents a relaxation based on second order constraints and generates cuts that are valid inequalities for the disjunctive relaxations arising from the underlying combinatorial structure of the problem.
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Cooperative network design
TL;DR: Numerical results demonstrate that the proposed Nash bargaining solution approach permits to allocate costs fairly to users in a reasonable computation time, thus representing a very effective framework for the design of efficient and stable networks.
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Controllability under positivity constraints of semilinear heat equations
Dario Pighin,Enrique Zuazua +1 more
TL;DR: In this paper, the authors prove controllability results for semilinear parabolic equations under positivity constraints on the control, when the time horizon is long enough, and extend the result to any initial datum and any target trajectory.
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Exact solution to the Bloch equations and application to the Hahn echo
TL;DR: It is found that even in the presence of expected B0 inhomogeneity, off-resonance effects can be removed from R2 measurements, when∥ω∥⩽0.5γB1, by fitting the exact solutions of the Bloch equations.
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Improving solver success in reaching feasibility for sets of nonlinear constraints
Walid Ibrahim,John W. Chinneck +1 more
TL;DR: A range of computationally cheap constraint consensus algorithms that move from a given initial point to a better final point that is then passed to the nonlinear solver, and a new initial point placement heuristic for use when an initial point is not provided by the modeller.
References
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Book
AMPL: a mathematical programming language
Robert Fourer,Brian W. Kernighan +1 more
TL;DR: A translator is implemented that takes as input a linear AMPL model and associated data, and produces output suitable for standard linear programming optimizers.
Book ChapterDOI
On the development of a general algebraic modeling system in a strategic planning environment
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