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...

A deterministic global optimization algorithm is proposed for locating the global minimum of generalized geometric (signomial) problems (GGP). By utilizing an exponential variable transformation the initial nonconvex problem (GGP) is reduced to a (DC) programming problem where both the constraints and the objective are decomposed into the diierence of two convex functions. A convex relaxation o...

In this thesis, we analyze state-of-art techniques for analog circuit sizing and compare them on various metrics. We ascertain that a methodology which improves the accuracy of sizing without increasing the run time or the designer effort is a contribution. We argue that the accuracy of geometric programming can be improved without adversely influencing the run time or increasing the designer’s...

The purpose of this paper is to develop certain geometric results concerning the feasible regions of Semideenite Programs, called here Spectrahedra. We rst develop a characterization for the faces of spectrahedra. More speciically, given a point x in a spectrahedron, we derive an expression for the minimal face containing x. Among other things, this is shown to yield characterizations for extre...

In this paper we introduce a visual approach to functional programming with PLaSM, a design language used for geometric programming and the parametric generation of CAD models. A visual diagram is generated according to very few simple rules, and may be used both for automatically generating the corresponding PLaSM code and for the specification and distribution of computer tasks to be concurre...

Let IP denote the family of integer programs of the form Min cx : Ax = b, x 2 N n obtained by varying the right hand side vector b but keeping A and c xed. A test set for IP is a set of vectors in Z n such that for each non-optimal solution to a program in this family, there is at least one element g in this set such that ? g has an improved cost value as compared to. We describe a unique minim...

We make use of a result of Hurwitz and Reznick [8] [19], and a consequence of this result due to Fidalgo and Kovacec [5], to determine a new sufficient condition for a polynomial f ∈ R[X1, . . . , Xn] of even degree to be a sum of squares. This result generalizes a result of Lasserre in [10] and a result of Fidalgo and Kovacec in [5], and it also generalizes the improvements of these results gi...

We develop in this article a geometric approach to duality in Multiple Objective Linear Programming. This approach is based on a very old idea, the duality of polytopes, which can be traced back to the old Greeks. We show that there is an inclusion reversing one-to-one map between the minimal faces of the image of the primal objective and the maximal faces of the image of the dual objective map.