. Many problems in engineering analysis and design can be cast as convex optimization problems, often nonlinear and nondifferentiable. We give a high-level description of recently developed interior-point methods for convex optimization, explain how problem structure can be exploited in these algorithms, and illustrate the general scheme with numerical experiments. To give a rough idea of the efficiencies obtained, we are able to solve convex optimization problems with over 1000 variables and 10000 constraints in around 10 minutes on a workstation. Keywords. Optimization, numerical methods, linear programming, optimal control, robust control, convex programming, interior-point methods, FIR filter design, conjugate gradients 1. INTRODUCTION Many problems in engineering analysis and design can be cast as convex optimization problems, i.e., min f 0 (x) s.t. f i (x) 0; i = 1; : : : ; L; where the functions f i are convex. It is widely known that such problems have desirable properties,...

The optimal control of a CVD reactor is an important issue in the semiconductor industry. In this report we examine the issues of using large-scale optimization methods for the solution of the CVD optimal control problem. We consider using the TWAFER analysis code to compute the temperature distributions inside a CVD reactor and coupling it with a nonlinear optimization code to find the optimal power curves which achieve a specified target temperature in minimum time. A model problem is numerically tested and analyzed to give insight into our proposed method. The test results indicate that this approach can yield excellent predictions for the optimal power curves. 3/4 1. Introduction An important resource in the semiconductor sition (CVD) furnaces for the fabrication of industry is the use of chemical vapor wafers. These furnaces are used to heat up a silicon wafer to a specified temperature so that certain chemical reactions may occur, thereby creating a circuit pattern on the waf...