Computer-aided design via optimization : A review

Many design problems, including control design problems, involve infinite dimensional constraints of the form @f(z, @a) @? 0 for all @a @e A, where @a denotes time or frequency or a parameter vector. In other design problems, tuning or trimming of certain parameters, after manufacture of the system, is permitted; the corresponding constraint is that for each @a in A there exists a value @t (of the tuning parameter) in a permissible set T such that @f(z, @a, t) < 0. Recent algorithms for solving design problems having such constraints are summarized.

[1]  R. Mifflin Semismooth and Semiconvex Functions in Constrained Optimization , 1977 .

[2]  F. Clarke Generalized gradients and applications , 1975 .

[3]  E. Polak,et al.  Theoretical and computational aspects of the optimal design centering, tolerancing, and tuning problem , 1979 .

[4]  David Q. Mayne,et al.  Solving nonlinear inequalities in a finite number of iterations , 1981 .

[5]  Boris Polyak,et al.  Constrained minimization methods , 1966 .

[6]  David Q. Mayne,et al.  Computer aided design of control systems via optimization , 1979 .

[7]  D. Mayne,et al.  An algorithm for optimization problems with functional inequality constraints , 1976 .

[8]  C. C. Gonzaga,et al.  On Constraint Dropping Schemes and Optimality Functions for a Class of Outer Approximations Algorithms , 1979 .

[9]  D. Mayne,et al.  On the finite solution of nonlinear inequalities , 1979 .

[10]  V. Zakian,et al.  Design of dynamical and control systems by the method of inequalities , 1973 .

[11]  B. Eaves,et al.  Generalized Cutting Plane Algorithms , 1971 .

[12]  E. Polak An implementable algorithm for the optimal design centering, tolerancing, and tuning problem , 1982 .

[13]  C. C. Gonzaga,et al.  An improved algorithm for optimization problems with functional inequality constraints , 1980 .

[14]  Kenneth O. Kortanek,et al.  Numerical treatment of a class of semi‐infinite programming problems , 1973 .

[15]  D. Q. Mayne,et al.  Computer-aided design of control systems via optimisation , 1979 .

[16]  K. R. Gehner,et al.  Necessary and Sufficient Optimality Conditions for the Fritz John Problem with Linear Equality Constraints , 1974 .

[17]  David Q. Mayne,et al.  Combined phase I—phase II methods of feasible directions , 1979, Math. Program..

[18]  D. Mayne,et al.  An outer approximations algorithm for computer-aided design problems , 1979 .