We revisit the extremum seeking scheme whose local stability properties were analyzed in (Krstić and Wang, 2000) and propose its simplified version that still achieves extremum seeking. We show under slightly stronger conditions that this simplified scheme achieves extremum seeking from arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted...

We study periodic torus orbits on space of lattices. Using the action of the group of adelic points of the underlying tori, we define a natural equivalence relation on these orbits; for rank 3 lattices, we show that the equivalence classes become uniformly distributed. This is a cubic analogue of Duke’s theorem about the distribution of closed geodesics on the modular surface: suitably interpre...

Stable matching problems have several practical applications. If preference lists are truncated and contain ties, finding a stable matching with maximal size is computationally difficult. We address this problem using a local search technique, based on Adaptive Search and present experimental evidence that this approach is much more efficient than state-of-the-art exact and approximate methods....

Parsing techniques based on rules defining grammaticality are difficult to use with authentic inputs, which are often grammatically messy. Instead, the APRIL system seeks a labelled tree su~cture which maximizes a numerical measure of conformity to statistical norms derived flom a sample of parsed text. No distinction between legal and illegal trees arises: any labelled tree has a value. Becaus...

Constraints on downside risk, measured by shortfall probability, expected shortfall, semi-variance etc., lead to optimal asset allocations which differ from the meanvariance optimum. The resulting optimization problem can become quite complex as it exhibits multiple local extrema and discontinuities, in particular if we also introduce constraints restricting the trading variables to integers, c...

In this paper we present a practical, efficient and robust algorithm for detecting the global convergence in any asynchronous iterative process. A proven theoretical version, together with a first practical version, was presented in [1]. However, the main drawback of that first practical version was to require the determination of the maximal communication time between any couple of nodes in th...

In this paper we arrive at explicit formulae for the innnitesi-mal generators of the action of a complex simple Lie group G on the mani-fold M = G=P where P is a maximal parabolic subgroup. These formulae are obtained by assuming that local coordinates on M are furnished by the nilpotent subalgebra n complementary to the maximal parabolic subalgebra p corresponding to P. For the classical isoge...

In many resource allocation problems, a centralized controller needs to award some resource to a user selected from a collection of distributed users with the goal of maximizing the utility the user would receive from the resource. This can be modeled as the controller computing an extremum of the distributed users’ utilities. The overhead rate necessary to enable the controller to reproduce th...

The research of its convergence of Mean Shift algorithm is the foundation of its application. Comaniciu and Li Xiang-ru have respectively provided the proof for the convergence of Mean Shift but they both made a mistake in their proofs. In this paper, the imprecise proofs existing in some literatures are firstly pointed out. Then, the local convergence is proved in a new way and the condition o...

We consider the problem of finding values of A3(n, d), i.e. the maximal size of a ternary code of length n and minimum distance d. Our approach is based on a search for good lower bounds and a comparison of these bounds with known upper bounds. Several lower bounds are obtained using a genetic local search algorithm. Other lower bounds are obtained by constructing codes. For those cases in whic...