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Efficient Convex Optimization For Engineering Design
, 1994
"... . Many problems in engineering analysis and design can be cast as convex optimization problems, often nonlinear and nondifferentiable. We give a highlevel description of recently developed interiorpoint methods for convex optimization, explain how problem structure can be exploited in these algori ..."
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Cited by 21 (13 self)
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. Many problems in engineering analysis and design can be cast as convex optimization problems, often nonlinear and nondifferentiable. We give a highlevel description of recently developed interiorpoint 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, interiorpoint 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,...
Optimal Control of a CVD Reactor for Prescribed Temperature Behavior
, 1995
"... The optimal control of a CVD reactor is an important issue in the semiconductor industry. In this report we examine the issues of using largescale optimization methods for the solution of the CVD optimal control problem. We consider using the TWAFER analysis code to compute the temperature distribu ..."
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The optimal control of a CVD reactor is an important issue in the semiconductor industry. In this report we examine the issues of using largescale 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...