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The paper discusses the applicability of the piecewise-ellipsoidal approximation (PEA) to the acceptability region for solution of various design problems. The PEA technique, originally developed and tested for linear discrete circuits described in the frequency domain, is briefly reviewed. It is shown that PEA is a generic mathematical method and its applicability is extended to linear and nonlinear systems (not necessary electrical) described in time or frequency domains. The architecture of a software implementing the technique is introduced and approximations to the acceptability regions for the given design specifications for integrated circuits (CMOS amplifier, clock driver) and multidomain systems (servomechanism) are constructed and their accuracy checked. Then, some standard optimal-design algorithms (i.e., worst case parametric yield maximization, yield versus cost optimization) are redesigned to exploit the PEA properties (e.g., local convexity/concavity) and make them more effective. The algorithms are confronted with design problems, and quality of the resulting designs is assessed.