Optimization Problems with Physical Conditions

Abstract

In this chapter, the general mathematical theory presented in the previous chapter is applied to problems encountered in hadron physics. We start by bringing a generic physical situation to the canonical form, by performimg the conformal mapping of the analyticity domain onto the interior of the unit disk. Then we explain the procedure of constructing an outer function from its modulus on the boundary for a typical case encountered in many physical situations. For completeness, we also briefly discuss the construction in the case of matrix-valued analytic functions. Several optimization problems of physical interest are then treated, using the technique of Lagrange multipliers and the duality theorem in \(L^2\) and \(L^\infty \) norms. We discuss also the method of conformal mapping for extending the convergence domain and improving the convergence rate of power series. The chapter ends with a brief review of applications, presented in a historical perspective.