On iterated minimization in nonconvex optimization

In dynamic programming and decomposition methods one often applies an iterated minimization procedure. The problem variables are partitioned into several blocks, say x and y. Treating y as a parameter, the first phase consists of minimization with respect to the variable x. In a second phase the minimization of the resulting optimal value function depending on y is considered. In this paper we treat this basic idea on a local level. It turns out that strong stability (in the sense of Kojima) in the first phase is a natural assumption. In order to show that the iterated local minima of the parametric problem lead to a local minimum for the whole problem, we use a generalized version of a positive definiteness criterion of Fujiwara-Han-Mangasarian

540 mW of blue output power at 425 nm generated by intracavity frequency doubling an upconversion-pumped Er3+: YLiF4 laser

We report efficient room-temperature continuous-wave intracavity frequency doubling of an upconversion-pumped Er(1%):YLiF4 laser at 850 nm. A titanium-sapphire laser was used for excitation of the S-4(3/2)-- \u3e I-4(13/2) transition in erbium. The maximum laser output power at 850 nm was 1200 mW. Intracavity frequency doubling the fundamental wave utilizing lithium triborate as nonlinear crystal yielded a maximum second-harmonic output power of 540 mW at 425 nm