Projection methods in conic optimization

There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of applications in science, finance and engineering. This chapter reviews some of these algorithms, emphasizing the so-called regularization algorithms for linear conic optimization, and applications in polynomial optimization. This is a presentation of the material of several recent research articles; we aim here at clarifying the ideas, presenting them in a general framework, and pointing out important techniques

Synchronous precipitation reduction in the American Tropics associated with Heinrich 2

Abstract During the last ice age temperature in the North Atlantic oscillated in cycles known as Dansgaard-Oeschger (D-O) events. The magnitude of Caribbean hydroclimate change associated with D-O variability and particularly with stadial intervals, remains poorly constrained by paleoclimate records. We present a 3.3 thousand-year long stalagmite δ18O record from the Yucatan Peninsula (YP) that spans the interval between 26.5 and 23.2 thousand years before present. We estimate quantitative precipitation variability and the high resolution and dating accuracy of this record allow us to investigate how rainfall in the region responds to D-O events. Quantitative precipitation estimates are based on observed regional amount effect variability, last glacial paleotemperature records, and estimates of the last glacial oxygen isotopic composition of precipitation based on global circulation models (GCMs). The new precipitation record suggests significant low latitude hydrological responses to internal modes of climate variability and supports a role of Caribbean hydroclimate in helping Atlantic Meridional Overturning Circulation recovery during D-O events. Significant in-phase precipitation reduction across the equator in the tropical Americas associated with Heinrich event 2 is suggested by available speleothem oxygen isotope records