Modeling language

Abstract: The most widely used is GAMS, which is specifically designed for Further details on GAMS can be found in the GAMS User's Guide. The GAMS User's Guide. Mathematical Programming, 87:153–176, 2000. (4). A. Brooke, D. Kendrick, and A. Meeraus. GAMS: A User's Guide. The Scientific Press, South San Francisco. JuMP is an open-source modeling language that allows users to express a wide D. Kendrick, A. Meeraus, and R. Raman, GAMS: A User's Guide, Scientific.

Abstract: We present CasADi, an open-source software framework for numerical optimization. CasADi is a general-purpose tool that can be used to model and solve optimization problems with a large degree of flexibility, larger than what is associated with popular algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo. Of special interest are problems constrained by differential equations, i.e. optimal control problems. CasADi is written in self-contained C++, but is most conveniently used via full-featured interfaces to Python, MATLAB or Octave. Since its inception in late 2009, it has been used successfully for academic teaching as well as in applications from multiple fields, including process control, robotics and aerospace. This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last 7 years.

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.

Abstract: This paper describes a computer system for understanding English. The system answers questions, executes commands, and accepts information in an interactive English dialog. It is based on the belief that in modeling language understanding, we must deal in an integrated way with all of the aspects of language—syntax, semantics, and inference. The system contains a parser, a recognition grammar of English, programs for semantic analysis, and a general problem solving system. We assume that a computer cannot deal reasonably with language unless it can understand the subject it is discussing. Therefore, the program is given a detailed model of a particular domain. In addition, the system has a simple model of its own mentality. It can remember and discuss its plans and actions as well as carrying them out. It enters into a dialog with a person, responding to English sentences with actions and English replies, asking for clarification when its heuristic programs cannot understand a sentence through the use of syntactic, semantic, contextual, and physical knowledge. Knowledge in the system is represented in the form of procedures, rather than tables of rules or lists of patterns. By developing special procedural representations for syntax, semantics, and inference, we gain flexibility and power. Since each piece of knowledge can be a procedure, it can call directly on any other piece of knowledge in the system.