Differential optimization in finite-dimensional spaces

Finite Dimensional Generating Spaces of Quasi-Norm Family

In this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~The idea of equivalent quasi-norm families is introduced.~Riesz lemma is established in this space.~Finally,~we re-define B-S fuzzy norm and prove that it induces a generating space of quasi-norm family.

Nonlinear Approximation in Finite-Dimensional Spaces

Nonlinear approximation is utilized in many numerical algorithms. In this paper, we shall consider certain problems of nonlinear approximation which arise in image processing. This includes approximation using m terms from a dictionary of functions and greedy algorithms for approximation from such a dictionary. Let X be a Banach space and let ⊂ X be a subset of X whose linear span is dense in X...

Euclidean Structure in Finite Dimensional Normed Spaces

Optimization in infinite-dimensional Hilbert spaces

We consider the minimization of convex functionals on a real Hilbert space. The requisite theory is reviewed, and concise proofs of the relevant results are given.

Particle Swarm Optimization in High Dimensional Spaces

Global optimization methods including Particle Swarm Optimization are usually used to solve optimization problems when the number of parameters is small (hundreds). In the case of inverse problems the objective (or fitness) function used for sampling requires the solution of multiple forward solves. In inverse problems, both a large number of parameters, and very costly forward evaluations hamp...