… In this paper convex optimization techniques are employed for convex optimization problems
in infinite dimensional Hilbert spaces. A first order optimality condition is given. Let f : Rn → …

… , convex optimization techniques are employed for convex optimization problems in infinite
dimensional Hilbert spaces. … Lastly, we have given optimization conditions involving positive …

… We consider the method for constrained convex optimization in a Hilbert space, consisting
of a step in the direction opposite to an ek-subgradient of the objective at a current iterate, fol…

… BASIC PROPER TIES OF HILBERT SPACES In this chapter we present a condensed version
of those properties of Hilbert Spaces which are basic to optimization theory in our view. A …

… restrictive to assume that the domain of the optimization variables is indeed a Hilbert space.
… Here, we adopt the modern standpoint on moment problems using convex optimization [30, …

… feature space [10]. This space is known as the reproducing kernel Hilbert space (RKHS)
and is usually an infinitedimensional linear space of functions. Moreover, it is well known that …

… , in general, cannot be extended to arbitrary Banach spaces. … theory and methods of convex
optimization have not been … , convex analysis and monotone operators in Hilbert spaces, and …

… or Hilbert spaces extend into this nonlinear setting. On the other hand some areas of convex
… We will describe an application of convex optimization in Hadamard spaces to computa…

… for convex problems in Hilbert spaces, and demonstrate its application on a particular class
of problems, namely a convex … for convex optimization in Hilbert spaces, Numer. Funct. Anal. …

… Let C be a closed and convex subset of a real Hilbert space H. Given x ∈ … Hilbert space
and let C be a nonempty, closed, and convex subset of H. Let h : C → ℝ be a real-valued convex …