The stress singularity of a sharp wedge contacting a frictionless half plane can be avoided by changing the wedge shape. Shape optimization is accomplished with the geometric strain method (GSM), an optimality criterion method. Several numerical examples are provided for different materials in the wedge and half plane to avoid stress singularity near the sharp corner of the wedge. Optimum wedge...

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 ...

In this paper we consider the problem of optimizing a piecewise-linear objective function over a non-convex domain. In particular we do not allow the solution to lie in the interior of a prespeciied region R. We discuss the geometrical properties of this problems and present algorithms based on combinatorial arguments. In addition we show how we can construct quite complicated shaped sets R whi...

We study the problem of maintaining a (1+2)-factor approximation of the diameter of a stream of points under the sliding window model. In one dimension, we give a simple algorithm that only needs to store O( 1 2 logR) points at any time, where the parameter R denotes the “spread” of the point set. This bound is optimal and improves Feigenbaum, Kannan, and Zhang’s recent solution by two logarith...

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 ...

This thesis has two main parts. The first part deals with the stage illumination problem. Given a stage represented by a line segment L and a set of lightsources represented by a set of points S in the plane, assign powers to the lightsources such that every point on the stage receives a sufficient amount, e.g. one unit, of light while minimizing the overall power consumption. By assuming that ...

This paper illustrates the fundamental connection between nonconvex quadratic optimization and copositive optimization—a connection that allows the reformulation of nonconvex quadratic problems as convex ones in a unified way. We focus on examples having just a few variables or a few constraints for which the quadratic problem can be formulated as a copositive-style problem, which itself can be...

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...

This paper studies state quantization schemes for feedback stabilization of linear control systems with limited information. The focus is on designing the least destabilizing quantizer subject to a given information constraint. We explore several ways of measuring the destabilizing effect of a quantizer on the closed-loop system, including (but not limited to) the worst-case quantization error....