Strong and weak minima of functionals in a real hilbert space
I. Glnchev · Optimization · 1992
For each real infinitely dimensional Hilbert space X a weakly continuous function f:X → R is constructed, possessing at x 0=0 a strong minimum (i.e. a local minimum with respeel to the norm topology), which is not a weak minimum (i.e. a local minimum with respect to the weak topology). For the given example different convexity properties are discussed.