Analysis of a class of proxy problems (Q801816)

This paper contains 4 lemmas, 3 theorems and 2 corollaries to show that minimization problems involving objective functions of the form \(g(x)+\phi (u(x))\), where \(\phi\) is concave, can be solved by means of proxy problems, the objective function of which is of the form \(g(x)+\lambda u(x)\). the authors also use the theorems to construct a counterexample to a theorem of \textit{N. Katoh} and \textit{t. Ibaraki} [ibid. 2, 62-65 (1983; Zbl 0506.90039)].