ABSTRACT
This chapter describes fundamental concepts and theory of optimization that are most relevant to physical design applications. It reviews the basic convex optimization models of linear programming, second-order cone programming, semidefinite programming, and geometric programming, as are the concept of convexity, optimality conditions, and Lagrangian relaxation. The chapter introduces the concept of robust optimization and illustrates a circuit optimization example its effectiveness. It describes the basic optimization concepts, models, and tools that are most relevant to circuit design applications, and in particular, to expose the reader to the types of nonlinear optimization problems that are “easy.” The problem of optimally choosing dual multipliers is always convex and is therefore amenable to efficient solution by the standard convex optimization techniques. For any convex optimization problem, the set of global optimal solutions is always convex. Lagrangian duality theory presented can also be used to derive convex relaxations of nonconvex optimization problems.
