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A theory of optimal worst-case design embodying centering, tolerancing, and tuning is presented. Some simplified problems and special cases are discussed. Projections and slack variables are used to explain some of the concepts. The worst-case tolerance assignment and design centering problem falls out as a special case. Practical implementation requires a reasonable and'relevant number of parameters and constraints to be identified to make the problem tractable. Two circuits, a simple low-pass filter and a realistic high-pass filter, are studied under a variety of different problem situations to illustrate both the benefits to be derived from our approach and the difficulties encountered in its implementation.