We study constrained and unconstrained optimization programs for nonconvex maximum eigenvalue functions. We show how second order techniques may be introduced as soon as it is possible to reliably guess the multiplicity of the maximum eigenvalue at a limit point. We examine in which way standard and projected Newton steps may be combined with a nonsmooth first-order method to obtain a globally ...

For regulating the dynamic nonholonomic mobile cart with parameter uncertainties, a time-varying robust control law is derived to yield globally exponential convergence of carts position and orientation to the desired set point. The controller design relies on converting the carts dynamics to an advantageous form, and the robust linear feedback control laws steer the carts position and orientat...

Motivated by mathematical modeling, analog implementation and distributed simulation of neural networks, we present a definition of asynchronous dynamics of general CT dynamical systems defined by ordinary differential equations, based on notions of local times and communication times. We provide some preliminary results on globally asymptotical convergence of asynchronous dynamics for contract...

The problem of adaptive minimization of globally unknown functionals under constraints on the independent variable is considered in a stochastic framework. The CAM algorithm for vector problems is proposed. By resorting to the ODE analysis for analysing stochastic algorithms and singular perturbation methods, it is shown that the only possible convergence points are the constrained local minima...

We consider the fast solution of non{smooth optimization problems as resulting for example from the approximation of elliptic free boundary problems of obstacle or Stefan type. Combining well{known concepts of successive subspace correction methods with convex analysis, we derive a new class of multigrid methods which are globally convergent and have logarithmic bounds of the asymptotic converg...

more than 50% of the global population already lives in urban settlements which are projected to absorb almost all the global population growth to 2050, amounting to some additional three billion people. over the next decades the increase in rural population in many developing countries will be overshadowed by population flows to cities. rural populations globally are expected to peak at a leve...

While the Expectation-Maximization (EM) algorithm is a popular and convenient tool for mixture analysis, it only produces solutions that are locally optimal, and thus may not achieve the globally optimal solution. This paper introduces a new algorithm, based on the global optimization algorithm Model Reference Adaptive Search (MRAS), designed to produce globally-optimal solutions in the estimat...

A novel generalized theoretical result is presented that underpins the development of globally convergent first-order batch training algorithms which employ local learning rates. This result allows us to equip algorithms of this class with a strategy for adapting the overall direction of search to a descent one. In this way, a decrease of the batch-error measure at each training iteration is en...

A nonlinear, closed-loop, time-invariant controller that globally stabilizes an underactuated marine vehicle on a straight course is proposed. Traditional surface vessel linear course tracking autopilots are designed applying linear control methods on the linearized model, thus yielding only local results. Indeed due to the underactuated nature of the system, the model cannot be feedback linear...