GLODS: Global and Local Optimization using Direct Search

Locating and identifying points as global minimizers is, in general, a hard and time-consuming task. Difficulties increase in the impossibility of using the derivatives of the functions defining the problem. In this work, we propose a new class of methods suited for global derivative-free constrained optimization. Using direct search of directional type, the algorithm alternates between a search step, where potentially good regions are located, and a poll step where the previously located promising regions are explored. This exploitation is made through the launching of several instances of directional direct searches, one in each of the regions of interest. Differently from a simple multistart strategy, direct searches will merge when sufficiently close. The goal is to end with as many direct searches as the number of local minimizers, which would easily allow locating the global extreme value. We describe the algorithmic structure considered, present the corresponding convergence analysis and report numerical results, showing that the proposed method is competitive with currently commonly used global derivative-free optimization solvers.

Magma flow pattern in dykes of the Azores revealed by ansiotropy of magnetic susceptibility

The localization of magma melting areas at the lithosphere bottom in extensional volcanic domains is poorly understood. Large polygenetic volcanoes of long duration and their associated magma chambers suggest that melting at depth may be focused at specific points within the mantle. To validate the hypothesis that the magma feeding a mafic crust, comes from permanent localized crustal reservoirs, it is necessary to map the fossilized magma flow within the crustal planar intrusions. Using the AMS, we obtain magmatic flow vectors from 34 alkaline basaltic dykes from São Jorge, São Miguel and Santa Maria islands in the Azores Archipelago, a hot-spot related triple junction. The dykes contain titanomagnetite showing a wide spectrum of solid solution ranging from Ti-rich to Ti-poor compositions with vestiges of maghemitization. Most of the dykes exhibit a normal magnetic fabric. The orientation of the magnetic lineation k1 axis is more variable than that of the k3 axis, which is generally well grouped. The dykes of São Jorge and São Miguel show a predominance of subhorizontal magmatic flows. In Santa Maria the deduced flow pattern is less systematic changing from subhorizontal in the southern part of the island to oblique in north. These results suggest that the ascent of magma beneath the islands of Azores is predominantly over localized melting sources and then collected within shallow magma chambers. According to this concept, dykes in the upper levels of the crust propagate laterally away from these magma chambers thus feeding the lava flows observed at the surface.