An interactive linear programming-based method is proposed for optimization problems in worst case circuit design and device modeling. The method maximizes the impact of a single constrained Linear Programming (LP) step on a nonlinear design problem. The method thus becomes, for large problems, an economic first-order alternative to expensive completely convergent optimization algorithms. By fully exploiting the customary investment of IC designers in large change (and/or adjoint) sensitivity computation, the interactive (and inexpensive) LP design subproblem becomes a paradigm of the larger nonlinear design problem, in which critical tradeoffs and limitations become evident. In comparison with previously reported design methods, the key points of novelty are 1) the interactive role of the user in searching for a maximally effective LP step, 2) the combination of function minimization, step size minimization, and function inequality constraints in the LP step, and 3) linear prediction of all performance objective functions. Examples are given of the application of the method to the design and modeling of practical digital logic circuits.