A Geometric programming (GP) is a type of mathematical problem characterized by objective and constraint functions that have a special form. Many methods have been developed to solve large scale engineering design GP problems. In this paper GP technique has been used to solve multi-objective GP problem as a vector optimization problem. The duality theory for lexicographic geometric programming ...

There is a proliferation of geometric algorithms and data types with no existing mechanism to unify geometric programming in C++. The geometry template library (GTL) provides geometry concepts and concept mapping through traits as well as algorithms parameterized by conceptual geometric data type to provide a unified library of fundamental geometric algorithms that is interoperable with existin...

An algebra for geometric reasoning is developed that is amenable to software implementation. The features of the algebra are chosen to support geometric programming of the variety found in computer graphics and computer aided geometric design applications. The implementation of the algebra in C++ is described, and several examples illustrating the use of this software are given.

This paper concerns a method for digital circuit optimization based on formulating the problem as a geometric program (GP) or generalized geometric program (GGP), which can be transformed to a convex optimization problem and then very efficiently solved. We start with a basic gate scaling problem, with delay modeled as a simple resistor-capacitor (RC) time constant, and then add various layers ...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii List of Abbreviations Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xiii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xiv CHAPTER 1: Introduction . . . . . . . . . . . . . . . . . . ....

Delay of VLSI circuit components can be controlled by varying their sizes. In other words, performance of VLSI circuits can be optimized by changing the sizes of the circuit components. In this paper, we define a special type of geometric program called unary geometric program. We show that under the Elmore delay model, several commonly used formulations of the circuit component sizing problem ...

Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are estimating of actual values. This paper develops a solution procedure to solve nonlinear programming problems using GP technique by splitting the cost coeffi...

Recently, various algebraic integer programming (IP) solvers have been proposed based on the theory of Gröbner bases. The main difficulty of these solvers is the size of the Gröbner bases generated. In algorithms proposed so far, large Gröbner bases are generated by either introducing additional variables or by considering the generic IP problem IPA,C . Some improvements have been proposed such...