Algebraic modelling languages have gained wide acceptance and use in Mathematical Programming by researchers and practitioners. At a basic level, stochastic programming models can be defined using these languages by constructing their deterministic equivalent. Unfortunately, this leads to very large model data instances. We propose a direct approach in which the random values of the … Read more
Every multistage stochastic programming problem with recourse (MSPR) contains a filtration process. In this research, we created a notation that makes the filtration process the central syntactic construction of the MSPR. As a result, we achieve lower redundancy and higher modularity than is possible with the mathematical notation commonly associated with stochastic programming. To experiment … Read more
The NEOS Server provides access to a variety of optimization resources via the Internet. The new Kestrel interface to the Server enables local modeling environments to request NEOS optimization services and retrieve the results for local visualization and analysis, so that users have the same convenient access to remote NEOS solvers as to those installed … Read more
Distributed computing technologies such as Web Services are growing rapidly in importance in today’s computing environment. In the area of mathematical optimization, it is becoming increasingly common to separate modeling languages from optimization solvers. In fact, the modeling language software, solver software, and data used to generate a model instance might reside on different machines … Read more
OOPS is an object oriented parallel solver using the primal dual interior point methods. Its main component is an object-oriented linear algebra library designed to exploit nested block structure that is often present is truly large-scale optimization problems. This is achieved by treating the building blocks of the structured matrices as objects, that can use … Read more
There are numerous algebraic modeling languages for generating linear programs and numerous solvers for computing solutions to linear programs. This proliferation of modeling languages and solvers is frustrating to modelers who find that only certain languages connect to certain solvers. One way to encourage modeler-solver compatibility is to use a standard representation of a problem … Read more
In the context of SQP methods or, more recently, of sequential semidefinite programming methods, it is common practice to construct a positive semidefinite approximation of the Hessian of the Lagrangian. The Hessian of the augmented Lagrangian is a suitable approximation as it maintains local superlinear convergence under appropriate assumptions. In this note we give a … Read more
This paper draws from our experience in developing the AMPL modeling language, to show where numerical issues have been crucial to modeling language design and where modeling language advances have strongly influenced the design of solvers. CitationProceedings of the 20th Biennial Conference on Numerical Analysis, Dundee, Scotland, D.F. Griffiths and G.A. Watson, eds., University of … Read more
In the paper it is shown how to utilize the flexibility in native Java arrays for matrix computations. Suitable datastructures for symmetric and sparse matrices are introduced. A disadvantage of the native Java arrays is shown when used as two-dimensional array for dense matrix computation. Numerical results show that the efficiency is not lost using … Read more
Automatic differentiation (AD) automatically transforms programs which calculate elementary functions into programs which calculate the gradients of these functions. Unlike other differentiation techniques, AD allows one to calculate the gradient of any function at the cost of at most 5 values of the function (in terms of time). Interval constraint programming (ICP) is a part … Read more