Generalized Solutions of Constrained Optimization Problems
Tomáš Roubı́ček · SIAM Journal on Control and Optimization · 1986
A constrained optimization problem on a uniform space X is considered. Under certain assumptions, the problem may be extended onto the completion of X with respect to the precompact modification of the original uniformity on X, which yields the generalized problem. It is shown that the solution of the perturbed classical problem (or of the penalized classical problem) converges to the solution of the generalized problem, which makes the generalized problem more convenient than the classical one. Finally, the general framework is demonstrated in special cases in normed linear spaces.