Since K is a
convex set, the line segment [[[omega].sub.k], [[omega].sub.k]] connecting [[omega].sub.k] and [[omega].sub.k] lies entirely inside K, and ([[omega].sub.k] - [[omega].sub.k]) is a feasible direction.
Each linear term in (7) corresponds to the projection onto the
convex set in the signal or Fourier domains in the Gerchberg algorithm.
If for every x, y [member of] I we need that x should be an end point of the path, then I reduces to a
convex set.
where [THETA] [subset] [R.sup.nxn] is a nonempty closed
convex set, [xi] is a random matrix whose probability distribution P is supported onset [OMEGA] [subset] [R.sup.nxn], and F is a smooth convex stochastic function on [THETA] x [OMEGA].
Let C and S* be the subclasses of S which are convex (f(D) is a
convex set) and starlike (f(D) is a starlike set with respect to the origin) respectively.
For example, it is well-known that every ||*||-closed (originally closed, strongly closed)
convex set is also [T.sub.w]-closed (weakly closed).
Recall that a convex space X is a nonempty
convex set with any topology that induces the Euclidean topology on the convex hulls of its finite subsets.
Since [OMEGA] is a
convex set and [bar.t], [t.sup.*] [member of] [OMEGA], we have