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It is shown that many engineering design problems can be formulated in terms of inequality constraints on the system response function(s) and on the design parameters. Any set of design variables for which these constraints are satisfied constitutes an acceptable design. There may be many acceptable designs or none at all. In either case it is possible to define a best or optimal design in a meaningful minimax sense. Such an optimal design is the solution of a related nonlinear programming problem involving the minimization of an easily determined objective function, subject to inequality constraints. Some suggested minimization techniques for solving such problems are briefly described. Two reasonably complex examples, using these methods, are presented: the first details the design of an under-water sonar system and the second describes the design of a wideband crystal filter.