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24
Convexity and Concavity Detection in Computational Graphs Tree Walks for Convexity Assessment
, 2008
"... Abstract. In this paper, we examine sets of symbolic tools associated to modeling systems for mathematical programming which can be used to automatically detect the presence or lack of convexity and concavity in the objective and constraint functions. As a consequence, convexity of the feasible set ..."
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Abstract. In this paper, we examine sets of symbolic tools associated to modeling systems for mathematical programming which can be used to automatically detect the presence or lack of convexity and concavity in the objective and constraint functions. As a consequence, convexity of the feasible set may be assessed to some extent. The coconut solver system [Sch04b] focuses on nonlinear global continuous optimization and possesses its own modeling language and data structures. The Dr.ampl [FO07] metasolver aims to analyze nonlinear diffentiable optimization models and hooks into the ampl Solver Library [Gay02]. The symbolic analysis may ◭ be supplemented with a numerical disproving phase when the former returns inconclusive results. We report numerical results using these tools on sets of test problems for both global and local optimization. 1.
SymbolicAlgebraic Computations in a Modeling Language for Mathematical Programming
, 2000
"... This paper was written for the proceedings of a seminar on "Symbolicalgebraic ..."
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This paper was written for the proceedings of a seminar on "Symbolicalgebraic
A Modeling Interface to NonLinear Programming Solvers  An instance: xMPS, the extended MPS format
, 2000
"... We present a ModelerOptimizer Interface (MOI) for general closed form NonLinear Programs (NLP), which can be used to to transfer NLPs in a clear and simple manner between optimization components in a distributed environment. We demonstrate how this interface allows rst order derivative informat ..."
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We present a ModelerOptimizer Interface (MOI) for general closed form NonLinear Programs (NLP), which can be used to to transfer NLPs in a clear and simple manner between optimization components in a distributed environment. We demonstrate how this interface allows rst order derivative information to be easily calculated on the optimizer's side, using automatic dierentiation, hence removing the bottleneck of communicating derivative information between the modeler and the optimizer. We also show how this interface directly corresponds to a le format for NLPs, the extended MPS format (xMPS). This format directly extends the standard MPS le format for linear and mixed integer programs to include NLPs and permits a standardized way of transferring benchmark problems. The format spares the modeler the tedious task of calculating derivative information with minimal extra work required by the optimizer and thus increases eciency. This work was originally done at Maximal Sof...
The NLPLIB Graphical User Interface
, 1998
"... This paper presents a Graphical User Interface (GUI) for nonlinear programming in MATLAB. The GUI gives easy access to all features in the NLPLIB (NonLinear Programming LIBrary) Toolbox; a set of MATLAB solvers, test problems, graphical and computational utilities for unconstrained and constrained o ..."
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This paper presents a Graphical User Interface (GUI) for nonlinear programming in MATLAB. The GUI gives easy access to all features in the NLPLIB (NonLinear Programming LIBrary) Toolbox; a set of MATLAB solvers, test problems, graphical and computational utilities for unconstrained and constrained optimization, quadratic programming, unconstrained and constrained nonlinear least squares and exponential sum øtting. NLPLIB TB, like the operations research toolbox OPERA TB, is a part of TOMLAB; an environment in MATLAB for research and teaching in optimization. TOMLAB currently solves small and medium size dense problems. Presently, NLPLIB TB implements more than 20 internal solvers. From NLPLIB TB it is possible to call solvers in the MATLAB Optimization Toolbox and generalpurpose solvers implemented in Fortran or C. Fortran and C solvers are called from MATLAB using a MEXøle interface. A problem is solved either by direct call to a parameter driven driver routine, or interactively, usi...
StAMPL: A filtrationoriented modeling tool for stochastic programming, tech
, 2006
"... This research investigates how to create a modeling tool specifically for stochastic programming problems with recourse. By taking advantage of the special structure these problems have, we produce a modeling language whose syntax is less redundant, more modular, and more expressive than the notatio ..."
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This research investigates how to create a modeling tool specifically for stochastic programming problems with recourse. By taking advantage of the special structure these problems have, we produce a modeling language whose syntax is less redundant, more modular, and more expressive than the notation commonly associated with stochastic programming. We then implement a system that can convert models written using this syntax to instances that can be solved using standard mechanisms. With this approach, we are able to represent models in a very clean, simple, and scalable format. 1.
TOMLAB  An Optimization Development Environment in MATLAB
, 1998
"... this paper we discuss the design and contents of TOMLAB. TOMLAB ..."
A Graphical User Interface for Nonlinear Programming in MATLAB
, 1998
"... This paper presents a Graphical User Interface (GUI) for nonlinear programming in MATLAB. The GUI gives easy access to all features in the NLPLIB (NonLinear Programming LIBrary) Toolbox; a set of MATLAB solvers, test problems, graphical and computational utilities for unconstrained and constraine ..."
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This paper presents a Graphical User Interface (GUI) for nonlinear programming in MATLAB. The GUI gives easy access to all features in the NLPLIB (NonLinear Programming LIBrary) Toolbox; a set of MATLAB solvers, test problems, graphical and computational utilities for unconstrained and constrained optimization, quadratic programming, unconstrained and constrained nonlinear least squares and exponential sum tting. NLPLIB TB, like the operations research toolbox OPERA TB, is a part of TOMLAB; an environment in MATLAB for research and teaching in optimization. TOMLAB currently solves small and medium size dense problems. Presently, NLPLIB TB implements more than 20 internal solvers. From NLPLIB TB it is possible to call solvers in the MATLAB Optimization Toolbox and generalpurpose solvers implemented in Fortran or C. Fortran and C solvers are called from MATLAB using a MEXle interface. A problem is solved either by direct call to a parameter driven driver routine, or interac...
Linking a Symbolic Solver to AMPL
"... symopt, a package of the computer algebra system reduce, is a symbolic solver for parametric mathematical programming. In order to make symopt applicable for interested people not familiar with reduce we implemented an interface to ampl  an algebraic modeling language for mathematical programm ..."
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symopt, a package of the computer algebra system reduce, is a symbolic solver for parametric mathematical programming. In order to make symopt applicable for interested people not familiar with reduce we implemented an interface to ampl  an algebraic modeling language for mathematical programming. In this paper the linking process of a symbolic solver to a algebraic modeling system is described.
The Numerical Algorithm Group, Ltd.
, 2011
"... Optimization, or Operational Research in general, nowadays plays an important role in our lives. No matter if you are a respected finance house or a student of mathematics, you have probably used some sort of optimization routines. The field itself has changed rapidly since linear programming was in ..."
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Optimization, or Operational Research in general, nowadays plays an important role in our lives. No matter if you are a respected finance house or a student of mathematics, you have probably used some sort of optimization routines. The field itself has changed rapidly since linear programming was introduced in the mid 1940s. More powerful computers allowed us to consider much more realistic and complex models using sophisticated algorithms. Whereas the input for linear programming problems is relatively simple, it is a much more delicate task in the case of general nonlinear programming. One way to tackle it is to introduce a specialised language for the problem description. In this tutorial we will focus on a particular one called AMPL which we have equipped with two of our NAG solvers, namely E04UFF and E04UGF. AMPL, A Mathematical Programming Language [3, 8], comes with several nice features packed together and it has earned considerable popularity. The language uses a common mathematical notation so it is easy to understand. Moreover, it includes an automatic differentiation package (a method to compute exact derivatives) therefore coding any derivatives can be completely avoided. This makes it ideal whenever you need to solve the problem fast. It is great for demonstrating or teaching as well as for rapid prototyping of mathematical models. Thus you can focus on optimization itself and not coding. It also unifies the interface for both setting the problems and solvers so you can test your solver on several problems or solve the same problem with several solvers without much effort. Thus a connection of AMPL and NAG software seems to be natural as it offers you the power of a modelling language together with NAG welltuned solvers. The tutorial is organised as follows. In the first two sections we introduce AMPL and a simple example written in the AMPL language. The 3rd section