In the field of inverse problems, one of the main benefits which can be drawn from primal-dual optimization approaches is that they do not require any linear operator inversion. In addition, they allow to split a convex objective function in a sum of simpler terms which can be dealt with individually either through their proximity operator or through their gradient if they correspond to smooth ...

We review the application of trajectory methods (not including homotopy methods) to global optimization problems. The main ideas and the most successful methods are described and directions of current and future research are indicated.

Query optimization is the most critical phase in query processing. In this paper, we try to describe synthetically the evolution of query optimization methods from uniprocessor relational database systems to data Grid systems through parallel, distributed and data integration systems. We point out a set of parameters to characterize and compare query optimization methods, mainly: (i) size of th...

Interior methods are an omnipresent, conspicuous feature of the constrained optimization landscape today, but it was not always so. Primarily in the form of barrier methods, interior-point techniques were popular during the 1960s for solving nonlinearly constrained problems. However, their use for linear programming was not even contemplated because of the total dominance of the simplex method....

In this chapter we present a selection of important algorithms for optimization problems with partial differential equations. The development and analysis of these methods is carried out in a Banach space setting. We begin by introducing a general framework for achieving global convergence. Then, several variants of generalized Newton methods are derived and analyzed. In particular, necessary a...