Search results for "Minimax"

Location of transition states and stable intermediates by MINIMAX/MINIMI optimization of synchronous transit pathways

1983

The MINIMAX/MINIMI concept for the location of transition states and/or stable intermediates of chemical reactions is introduced, based on the synchronous transit method. According to this strategy, minimization of quadratic synchronous transit path maxima or minima is achieved by constrained exhaustive optimization of internal coordinates. The method and its efficiency are demonstrated for two-dimensional model surfaces as well as for thermally allowed electrocyclic interconversions of cyclopropyl-/allyl-cation and cyclobutene-/butadiene (gauche) within the framework of MNDO-SCF calculations. Thus, in both cases a direct comparison with the exact solution determined by minimization of the …

On the adjoint group of some radical rings

1997

A ring R is called radical if it coincides with its Jacobson radical, which means that Rforms a group under the operation a ° b = a + b + ab for all a and b in R. This group is called the adjoint group R° of R. The relation between the adjoint group R° and the additive group R+ of a radical rin R is an interesting topic to study. It has been shown in [1] that the finiteness conditions “minimax”, “finite Prufer rank”, “finite abelian subgroup rank” and “finite torsionfree rank” carry over from the adjoint group to the additive group of a radical ring. The converse is true for the minimax condition, while it fails for all the other above finiteness conditions by an example due to Sysak [6] (s…

Applications and numerical convergence of the partial inverse method

2006

In 1983, J.E. Spingarn introduced what he called the Partial Inverse Method in the framework of Mathematical Programming. Since his initial articles, numerous applications have been given in various fields including Lagrangian multipliers methods, location theory, convex feasibility problems, analysis of data, economic equilibrium problems. In a first part of this paper we give a survey of these applications. Then by means of optimization problems relevant to location theory such as single and multifacility minimisum or minimax location problems, we examine the main advantages of the algorithm and we point out its drawbacks mainly concerning the rate of convergence. We study how different p…

The nonabelian tensor product of two soluble minimax groups

2010

A Note on Robust Intensity Estimation for Point Processes

1992

A robust intensity estimator based on independent marking is derived. A simulation study is made to convince that the new estimator works also in such cases where the usual estimators based on the distance methods do not work. Some truncated distributions are derived.

Minimax estimation with additional linear restrictions - a simulation study

1988

Let the parameter vector of the ordinary regression model be constrained by linear equations and in addition known to lie in a given ellipsoid. Provided the weight matrix A of the risk function has rank one, a restricted minimax estimator exists which combines both types of prior information. For general n.n.d. A two estimators as alternatives to the unfeasible exact minimax estimator are developed by minimizing an upper and a lower bound of the maximal risk instead. The simulation study compares the proposed estimators with competing least-squares estimators where remaining unknown parameters are replaced by suitable estimates.

Non-parametric Estimation of the Death Rate in Branching Diffusions

2002

We consider finite systems of diffusing particles in R with branching and immigration. Branching of particles occurs at position dependent rate. Under ergodicity assumptions, we estimate the position-dependent branching rate based on the observation of the particle process over a time interval [0, t]. Asymptotics are taken as t → ∞. We introduce a kernel-type procedure and discuss its asymptotic properties with the help of the local time for the particle configuration. We compute the minimax rate of convergence in squared-error loss over a range of Holder classes and show that our estimator is asymptotically optimal.

Adaptive Wavelet Methods for SPDEs

2014

We review a series of results that have been obtained in the context of the DFG-SPP 1324 project “Adaptive wavelet methods for SPDEs”. This project has been concerned with the construction and analysis of adaptive wavelet methods for second order parabolic stochastic partial differential equations on bounded, possibly nonsmooth domains \(\mathcal{O}\subset \mathbb{R}^{d}\). A detailed regularity analysis for the solution process u in the scale of Besov spaces \(B_{\tau,\tau }^{s}(\mathcal{O})\), 1∕τ = s∕d + 1∕p, α > 0, p ≥ 2, is presented. The regularity in this scale is known to determine the order of convergence that can be achieved by adaptive wavelet algorithms and other nonlinear appro…

Convex semi-infinite games

1986

This paper introduces a generalization of semi-infinite games. The pure strategies for player I involve choosing one function from an infinite family of convex functions, while the set of mixed strategies for player II is a closed convex setC inRn. The minimax theorem applies under a condition which limits the directions of recession ofC. Player II always has optimal strategies. These are shown to exist for player I also if a certain infinite system verifies the property of Farkas-Minkowski. The paper also studies certain conditions that guarantee the finiteness of the value of the game and the existence of optimal pure strategies for player I.

Noncooperative dynamic games for inventory applications: A consensus approach

2008

We focus on a finite horizon noncooperative dynamic game where the stage cost of a single player associated to a decision is a monotonically nonincreasing function of the total number of players making the same decision. For the single-stage version of the game, we characterize Nash equilibria and derive a consensus protocol that makes the players converge to the unique Pareto optimal Nash equilibrium. Such an equilibrium guarantees the interests of the players and is also social optimal in the set of Nash equilibria. For the multi-stage version of the game, we present an algorithm that converges to Nash equilibria, unfortunately not necessarily Pareto optimal. The algorithm returns a seque…