Projection Methods: Swiss Army Knives for Solving Feasibility and Best Approximation Problems with Halfspaces

We model a problem motivated by road design as a feasibility problem. Projections onto the constraint sets are obtained, and projection methods for solving the feasibility problem are studied. We present results of numerical experiments which demonstrate the efficacy of projection methods even for challenging nonconvex problems

Negotiating Concurrently with Unknown Opponents in Complex, Real-Time Domains

We propose a novel strategy to enable autonomous agents to negotiate concurrently with multiple, unknown opponents in real-time, over complex multi-issue domains. We formalise our strategy as an optimisation problem, in which decisions are based on probabilistic information about the opponents' strategies acquired during negotiation. In doing so, we develop the first principled approach that enables the coordination of multiple, concurrent negotiation threads for practical negotiation settings. Furthermore, we validate our strategy using the agents and domains developed for the International Automated Negotiating Agents Competition (ANAC), and we benchmark our strategy against the state-of-the-art. We find that our approach significantly outperforms existing approaches, and this difference improves even further as the number of available negotiation opponents and the complexity of the negotiation domain increases

A new Hamiltonian for the Topological BF phase with spinor networks

We describe fundamental equations which define the topological ground states in the lattice realization of the SU(2) BF phase. We introduce a new scalar Hamiltonian, based on recent works in quantum gravity and topological models, which is different from the plaquette operator. Its gauge-theoretical content at the classical level is formulated in terms of spinors. The quantization is performed with Schwinger's bosonic operators on the links of the lattice. In the spin network basis, the quantum Hamiltonian yields a difference equation based on the spin 1/2. In the simplest case, it is identified as a recursion on Wigner 6j-symbols. We also study it in different coherent states representations, and compare with other equations which capture some aspects of this topological phase.Comment: 40 page

A symmetric nodal conservative finite element method for the Darcy equation

This work introduces and analyzes novel stable Petrov-Galerkin EnrichedMethods (PGEM) for the Darcy problem based on the simplest but unstable continuous P1/P0 pair. Stability is recovered inside a Petrov-Galerkin framework where element-wise dependent residual functions, named multi-scale functions, enrich both velocity and pressure trial spaces. Unlike the velocity test space that is augmented with bubble-like functions, multi-scale functions correct edge residuals as well. The multi-scale functions turn out to be the well-known lowest order Raviart-Thomas basis functions for the velocity and discontinuous quadratics polynomial functions for the pressure. The enrichment strategy suggests the way to recover the local mass conservation property for nodal-based interpolation spaces. We prove that the method and its symmetric version are well-posed and achieve optimal error estimates in natural norms. Numerical validations confirm claimed theoretical results

Cooperatives for demand side management

We propose a new scheme for efficient demand side management for the Smart Grid. Specifically, we envisage and promote the formation of cooperatives of medium-large consumers and equip them (via our proposed mechanisms) with the capability of regularly participating in the existing electricity markets by providing electricity demand reduction services to the Grid. Based on mechanism design principles, we develop a model for such cooperatives by designing methods for estimating suitable reduction amounts, placing bids in the market and redistributing the obtained revenue amongst the member agents. Our mechanism is such that the member agents have no incentive to show artificial reductions with the aim of increasing their revenue

Consistent local projection stabilized finite element methods

This work establishes a formal derivation of local projection stabilized methods as a result of an enriched Petrov-Galerkin strategy for the Stokes problem. Both velocity and pressure finite element spaces are enhanced with solutions of residual-based local problems, and then the static condensation procedure is applied to derive new methods. The approach keeps degrees of freedom unchanged while gives rise to new stable and consistent methods for continuous and discontinuous approximation spaces for the pressure. The resulting methods do not need the use of a macro-element grid structure and are parameter-free. The numerical analysis is carried out showing optimal convergence in natural norms, and moreover, two ways of rendering the velocity field locally mass conservative are proposed. Some numerics validate the theoretical results