Shock ignition of thermonuclear fuel with high areal density

A novel method by C. Zhou and R. Betti [Bull. Am. Phys. Soc. 50, 140 (2005)] to assemble and ignite thermonuclear fuel is presented. Massive cryogenic shells are first imploded by direct laser light with a low implosion velocity and on a low adiabat leading to fuel assemblies with large areal densities. The assembled fuel is ignited from a central hot spot heated by the collision of a spherically convergent ignitor shock and the return shock. The resulting fuel assembly features a hot-spot pressure greater than the surrounding dense fuel pressure. Such a nonisobaric assembly requires a lower energy threshold for ignition than the conventional isobaric one. The ignitor shock can be launched by a spike in the laser power or by particle beams. The thermonuclear gain can be significantly larger than in conventional isobaric ignition for equal driver energy.     

New Inexact Parallel Variable Distribution Algorithms

We consider the recently proposed parallel variable distribution(PVD) algorithm of Ferris and Mangasarian [4] for solvingoptimization problems in which the variables are distributed amongp processors. Each processor has the primary responsibility forupdating its block of variables while allowing the remainingsecondary variables tochange in a restricted fashion along some easily computable directions.We propose useful generalizationsthat consist, for the general unconstrained case, of replacing exact global solution ofthe subproblems by a certain natural sufficient descent condition, and,for the convex case, of inexact subproblem solution in thePVD algorithm. These modifications are the key features ofthe algorithm that has not been analyzed before.The proposed modified algorithms are more practical andmake it easier to achieve good load balancing among the parallelprocessors.We present a general framework for the analysis of thisclass of algorithms and derive some new and improved linear convergence resultsfor problems with weak sharp minima of order 2 and strongly convex problems.We also show that nonmonotone synchronization schemesare admissible, which further improves flexibility of PVD approach.     

Convergence Analysis of Perturbed Feasible Descent Methods

We develop a general approach to convergence analysis of feasible descent methods in the presence of perturbations. The important novel feature of our analysis is that perturbations need not tend to zero in the limit. In that case, standard convergence analysis techniques are not applicable. Therefore, a new approach is needed. We show that, in the presence of perturbations, a certain -approximate solution can be obtained, where depends linearly on the level of perturbations. Applications to the gradient projection, proximal minimization, extragradient and incremental gradient algorithms are described.     

Perturbed Augmented Lagrangian Method Framework with Applications to Proximal and Smoothed Variants

Journal of Optimization Theory and Applications - We introduce a perturbed augmented Lagrangian method framework, which is a convenient tool for local analyses of convergence and rates of...     

Error bounds for proximal point subproblems and associated inexact proximal point algorithms

We study various error measures for approximate solution of proximal point regularizations of the variational inequality problem, and of the closely related problem of finding a zero of a maximal monotone operator. A new merit function is proposed for proximal point subproblems associated with the latter. This merit function is based on Burachik-Iusem-Svaiter’s concept of ε-enlargement of a maximal monotone operator. For variational inequalities, we establish a precise relationship between the regularized gap function, which is a natural error measure in this context, and our new merit function. Some error bounds are derived using both merit functions for the corresponding formulations of the proximal subproblem. We further use the regularized gap function to devise a new inexact proximal point algorithm for solving monotone variational inequalities. This inexact proximal point method preserves all the desirable global and local convergence properties of the classical exact/inexact method, while providing a constructive error tolerance criterion, suitable for further practical applications. The use of other tolerance rules is also discussed. Received: April 28, 1999 / Accepted: March 24, 2000?Published online July 20, 2000     

Forcing strong convergence of proximal point iterations in a Hilbert space

This paper concerns with convergence properties of the classical proximal point algorithm for finding zeroes of maximal monotone operators in an infinite-dimensional Hilbert space. It is well known that the proximal point algorithm converges weakly to a solution under very mild assumptions. However, it was shown by Güler [11] that the iterates may fail to converge strongly in the infinite-dimensional case. We propose a new proximal-type algorithm which does converge strongly, provided the problem has a solution. Moreover, our algorithm solves proximal point subproblems inexactly, with a constructive stopping criterion introduced in [31]. Strong convergence is forced by combining proximal point iterations with simple projection steps onto intersection of two halfspaces containing the solution set. Additional cost of this extra projection step is essentially negligible since it amounts, at most, to solving a linear system of two equations in two unknowns. Received January 6, 1998 / Revised version received August 9, 1999?Published online November 30, 1999     

Determination of electron affinity of carbonyl radicals by means of negative ion mass spectrometry

Appearance energies of [M-H](-) ions from carbonyl compounds R-CO-R' (R,R' = H, CH(3), NH(2), OH) have been measured by means of negative ion mass spectrometry in resonant electron capture mode. Values of electron affinity of the corresponding radicals, CH(2)&dbond;C(X)O, NH&dbond;C(X)O and O&dbond;C(X)O, have been determined. Copyright 1999 John Wiley & Sons, Ltd.     

Generalization of the Landau and Becker–Pommerenke Inequalities

Doklady Mathematics - A generalization of the Landau and Becker–Pommerenke inequalities, which are used to solve the problem of sharp domains of univalence in subclasses of holomorphic maps,...     

Critical solutions of nonlinear equations: stability issues

Mathematical Programming - It is known that when the set of Lagrange multipliers associated with a stationary point of a constrained optimization problem is not a singleton, this set may contain...