Parser for signomial and geometric programs

Abstract

A method and apparatus for parsing signomial and geometric programs, referred to herein as “the Parser”. Signomial and Geometric programming is a unique class of mathematical problems that is useful in the study of optimization problems. The Parser is a program designed to recognize and parse both signomial and geometric programs such that they may be accepted and solved by signomial and geometric program solvers. The Parser accepts an optimization problem from a user in the form of algebraic expressions. The Parser can then identify the problem as a signomial program and can further determine if it reduces to a geometric program. If either a signomial or geometric program exists, the Parser converts the algebraic expressions to a compact numeric format that can be accepted by a computer-aided solver. In the case of a geometric program, the solver may find a global solution to the optimization problem. However, in the case of signomial program, the solver may only find a local solution. The solution found by the solver is routed back to the Parser which reports it in a user-readable format.

Description

FIELD OF THE INVENTION [0001] The invention relates to the field of mathematical optimization, particularly the recognition and parsing of signomial and geometric programs such that they may be accepted and solved by signomial and geometric program solvers. BACKGROUND AND PRIOR ART [0002] Geometric programming is a unique class of mathematical problems that is useful in the study of optimization problems. The theory of Geometric Programming was initially developed over three decades ago and culminated in a publication by R. J. Duffin, E. L. Peterson and C. M. Zener (Geometric Programming, John Wiley & Sons, 1967). This publication describes a Geometric Program (GP) as an optimization problem having an objective function and a set of constraints which all must meet certain mathematical criteria. Perhaps the most important property of GPs is that they can be solved, with great efficiently, and globally, using recently developed interior-point methods. [0003] Since the impact of GPs ca...

AI Technical Summary

Benefits of technology

The invention is a program that can automatically convert and solve geometric programs, which are a type of mathematical problem. These programs are difficult to parse and require a lot of labor to modify. The invention provides a solution for automatically identifying and parsing these programs, which will save time and effort. The invention can be used in various fields such as engineering design, manufacturing, economics, statistics, and chemical equilibrium. The invention is a program that can automatically convert and solve geometric programs, which are a type of mathematical problem. These programs are difficult to parse and require a lot of labor to modify. The invention provides a solution for automatically identifying and parsing these programs, which will save time and effort.

Problems solved by technology

A very simple GP can be solved by hand, but more complex GPs effectively must be solved with the aid of computer programs.

For example, a very complex GP that may be used to describe a circuit design problem may have hundreds of optimization variables and thousands of constraints.

The mathematical operations needed to solve a GP of this magnitude would be too cumbersome to perform by hand; therefore, optimization programs are needed to solve most GPs.

Parsing a GP into this particular format typically requires extensive labor by one or more people.

Moreover, if this compact numeric format were generated by hand, any changes to the functions, variables or coefficients contained in the GP would require extensive labor to modify the problem.

However, these programs are very general in function and lack the sophistication required to identify and / or parse a GP.

Similarly, there is a need for a parser program that can identify and parse a GP because current optimization software tools lack the ability to accomplish these tasks.

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