A Ky Fan minimax inequality for quasiequilibria on finite dimensional spaces

Several results concerning existence of solutions of a quasiequilibrium problem defined on a finite dimensional space are established. The proof of the first result is based on a Michael selection theorem for lower semicontinuous set-valued maps which holds in finite dimensional spaces. Furthermore this result allows one to locate the position of a solution. Sufficient conditions, which are easier to verify, may be obtained by imposing restrictions either on the domain or on the bifunction. These facts make it possible to yield various existence results which reduce to the well known Ky Fan minimax inequality when the constraint map is constant and the quasiequilibrium problem coincides with an equilibrium problem. Lastly, a comparison with other results from the literature is discussed

Participatory GIS in Mapping Ecosystem Services: Two Case Studies from High-Biodiversity Regions in Italy and Peru

Assessing ecosystem services (ES) and mapping their values are of paramount importance. Here we present two case studies where the participatory mapping of social values of landscape ecosystem services is used in territories with high levels of cultural and biological diversity (Adamello Brenta Natural Park in Italy and the Alto Mayo basin in the Western Amazon, Peru). A mixed-method approach combining social geography fieldwork (participatory mapping) and desk work (GIS analyses) is adopted to improve ES mapping by including multiple actors and to increase awareness. Mapping ecosystem services is not just a technical task; it also highlights social implications of the cartographic process, a key issue in human geography. By taking into account the controversial and multiple roles of maps, and by involving actors in attributing values and mapping their spatial relations to landscape and ES, it is possible to enrich technical knowledge with local knowledge

Quasi-variational equilibrium models for network flow problems

We consider a formulation of a network equilibrium problem given by a suitable quasi-variational inequality where the feasible flows are supposed to be dependent on the equilibrium solution of the model. The Karushâ\u80\u93Kuhnâ\u80\u93Tucker optimality conditions for this quasi-variational inequality allow us to consider dual variables, associated with the constraints of the feasible set, which may receive interesting interpretations in terms of the network, extending the classic ones existing in the literature

Merit functions: a bridge between optimization and equilibria

In the last decades, many problems involving equilibria, arising from engineering, physics and economics, have been formulated as variational mathematical models. In turn, these models can be reformulated as optimization problems through merit functions. This paper aims at reviewing the literature about merit functions for variational inequalities, quasi-variational inequalities and abstract equilibrium problems. Smoothness and convexity properties of merit functions and solution methods based on them will be presented

A descent method for nonsmooth variational inequalities via regularization

In this paper we propose a descent method for solving variational inequality problems where the underlying operator is nonsmooth, locally Lipschitz, and monotone over a closed, convex feasible set. The idea is to combine a descent method for variational inequality problems whose operators are nonsmooth, locally Lipschitz, and strongly monotone, with the Tikonov-Browder regularization technique. Finally, numerical results are presented and discussed

Sentinel-2 Data Analysis and Comparison with UAV Multispectral Images for Precision Viticulture

Precision viticulture (PV) requires the use of technologies that can detect the spatial and temporal variability of vineyards and, at the same time, allow useful information to be obtained at sustainable costs. In order to develop a cheap and easy-to-handle operational monitoring scheme for PV, the aim of this work was to evaluate the possibility of using Sentinel-2 multispectral images for long-term vineyard monitoring through the Normalized Difference Vegetation Index (NDVI). Vigour maps of two vineyards located in northeastern Italy were computed from satellite imagery and compared with those derived from UAV multispectral images; their correspondence was evaluated from qualitative and statistical points of view. To achieve this, the UAV images were roughly resampled to 10 m pixel size in order to match the spatial resolution of the satellite imagery. Preliminary results show the potential use of open source Sentinel-2 platforms for monitoring vineyards, highlighting links with the information given in the agronomic bulletins and identifying critical areas for crop production. Despite the large differences in spatial resolution, the results of the comparison between the UAV and Sentinel-2 data were promising. However, for long-term vineyard monitoring at territory scale, further studies using multispectral sensor calibration and groundtruth data are required

Local cone approximations in mathematical programming

We show how to use intensively local cone approximations to obtain results in some fields of optimization theory as optimality conditions, constraint qualifications, mean value theorems and error bound

Optimization of HAART with genetic algorithms and agent-based models of HIV infection

Motivation: Highly Active AntiRetroviral Therapies (HAART) can prolong life significantly to people infected by HIV since, although unable to eradicate the virus, they are quite effective in maintaining control of the infection. However, since HAART have several undesirable side effects, it is considered useful to suspend the therapy according to a suitable schedule of Structured Therapeutic Interruptions (STI).In the present article we describe an application of genetic algorithms (GA) aimed at finding the optimal schedule for a HAART simulated with an agent-based model (ABM) of the immune system that reproduces the most significant features of the response of an organism to the HIV-1 infection.Results: The genetic algorithm helps in finding an optimal therapeutic schedule that maximizes immune restoration, minimizes the viral count and, through appropriate interruptions of the therapy, minimizes the dose of drug administered to the simulated patient.To validate the efficacy of the therapy that the genetic algorithm indicates as optimal, we ran simulations of opportunistic diseases and found that the selected therapy shows the best survival curve among the different simulated control groups.Availability: A version of the C-ImmSim simulator is available at http://www.iac.cnr.it/~filippo/c-ImmSim.htmlContact: [email protected]

Existence and solution methods for equilibria

Equilibrium problems provide a mathematical framework which includes optimization, variational inequalities, fixed-point and saddle point problems, and noncooperative games as particular cases. This general format received an increasing interest in the last decade mainly because many theoretical and algorithmic results developed for one of these models can be often extended to the others through the unifying language provided by this common format. This survey paper aims at covering the main results concerning the existence of equilibria and the solution methods for finding them

Future of oil and gas development in the western Amazon

The western Amazon is one of the world's last high-biodiversity wilderness areas, characterized by extraordinary species richness and large tracts of roadless humid tropical forest. It is also home to an active hydrocarbon (oil and gas) sector, characterized by operations in extremely remote areas that require new access routes. Here, we present the first integrated analysis of the hydrocarbon sector and its associated road-building in the western Amazon. Specifically, we document the (a) current panorama, including location and development status of all oil and gas discoveries, of the sector, and (b) current and future scenario of access (i.e. access road versus roadless access) to discoveries. We present an updated 2014 western Amazon hydrocarbon map illustrating that oil and gas blocks now cover 733 414 km(2), an area much larger than the US state of Texas, and have been expanding since the last assessment in 2008. In terms of access, we documented 11 examples of the access road model and six examples of roadless access across the region. Finally, we documented 35 confirmed and/or suspected untapped hydrocarbon discoveries across the western Amazon. In the Discussion, we argue that if these reserves must be developed, use of the offshore inland model-a method that strategically avoids the construction of access roads-is crucial to minimizing ecological impacts in one of the most globally important conservation regions