TWO NEW WEAK CONSTRAINT QUALIFICATIONS AND APPLICATIONS

We present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a CQ. This is done in the first new CQ, which we call the constant rank of the subspace component (CRSC) CQ. This new CQ also preserves many of the good properties of RCPLD, such as local stability and the validity of an error bound. We also introduce an even weaker CQ, called the constant positive generator (CPG), which can replace RCPLD in the analysis of the global convergence of algorithms. We close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods: sequential quadratic programming, augmented Lagrangians, interior point algorithms, and inexact restoration.

Concentration of floating biogenic material in convergence zones

Some organisms that live just below the sea surface (the neuston) are known more as a matter of curiosity than as critical players in biogeochemical cycles. The hypothesis of this work is that their existence implies that they receive some food from an upward flux of organic matter. The behaviour of these organisms and of the associated organic matter, hereafter mentioned as floating biogenic material (FBM) is explored using a global physical-biogeochemical coupled model, in which its generation is fixed to 1% of primary production, and decay rate is of the order of I month. The model shows that the distribution of FBM should depart rapidly from that of primary production.. and be more sensitive to circulation patterns than to the distribution of primary production. It is trapped in convergence areas, where it reaches concentrations larger by a factor 10 than in divergences, thus enhancing and inverting the contrast between high and low primary productivity areas. Attention is called on the need to better understand the biogeochemical processes in the first meter of the ocean, as they may impact the distribution of food for fishes, as well as the conditions for air-sea exchange and for the interpretation of sea color.

The Global Paleomonsoon as seen through speleothem records from Asia and the Americas

The regional monsoons of the world have long been viewed as seasonal atmospheric circulation reversal-analogous to a thermally-driven land-sea breeze on a continental scale. This conventional view of monsoons is now being integrated at a global scale and accordingly, a new paradigm has emerged which considers regional monsoons to be manifestations of global-scale seasonal changes in response to overturning of atmospheric circulation in the tropics and subtropics, and henceforth, interactive components of a singular Global Monsoon (GM) system. The paleoclimate community, however, tends to view 'paleomonsoon' (PM), largely in terms of regional circulation phenomena. In the past decade, many high-quality speleothem oxygen isotope (delta O-18) records have been established from the Asian Monsoon and the South American Monsoon regions that primarily reflect changes in the integrated intensities of monsoons on orbital-to-decadal timescales. With the emergence of these high-resolution and absolute-dated records from both sides of the Equator, it is now possible to test a concept of the 'Global-Paleo-Monsoon' (GPM) on a wide-range of timescales. Here we present a comprehensive synthesis of globally-distributed speleothem delta O-18 records and highlight three aspects of the GPM that are comparable to the modern GM: (1) the GPM intensity swings on different timescales; (2) their global extent; and (3) an anti-phased inter-hemispheric relationship between the Asian and South American monsoon systems on a wide range of timescales.