Displaying similar documents to “A generalized proximal point algorithm for the nonlinear complementarity problem ”

Depth Lower Bounds for Monotone Semi-Unbounded Fan-in Circuits

Jan Johannsen (2010)

RAIRO - Theoretical Informatics and Applications

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The depth hierarchy results for monotone circuits of Raz and McKenzie [5] are extended to the case of monotone circuits of semi-unbounded fan-in. It follows that the inclusions ⊆ ⊆ are proper in the monotone setting, for every ≥ 1.

Monotone (co)inductive types and positive fixed-point types

Ralph Matthes (2010)

RAIRO - Theoretical Informatics and Applications

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We study five extensions of the polymorphically typed lambda-calculus (system ) by type constructs intended to model fixed-points of monotone operators. Building on work by Geuvers concerning the relation between term rewrite systems for least pre-fixed-points and greatest post-fixed-points of positive type schemes (, non-nested positive inductive and coinductive types) and so-called retract types, we show that there are reduction-preserving embeddings even between systems of monotone...

Convolution property and exponential bounds for symmetric monotone densities

Claude Lefèvre, Sergey Utev (2013)

ESAIM: Probability and Statistics

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Our first theorem states that the convolution of two symmetric densities which are -monotone on (0∞) is again (symmetric) -monotone provided 0   ≤ 1. We then apply this result, together with an extremality approach, to derive sharp moment and exponential bounds for distributions having such shape constrained densities.

Bottleneck Capacity Expansion Problems with General Budget Constraints

Rainer E. Burkard, Bettina Klinz, Jianzhong Zhang (2010)

RAIRO - Operations Research

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This paper presents a unified approach for bottleneck capacity expansion problems. In the bottleneck capacity expansion problem, BCEP, we are given a finite ground set , a family of feasible subsets of and a nonnegative real capacity ĉ for all . Moreover, we are given monotone increasing cost functions for increasing the capacity of the elements as well as a budget . The task is to determine new capacities c ≥ ĉ such that the objective function given by...

Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects

Hedy Attouch, Paul-Émile Maingé (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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In the setting of a real Hilbert space , we investigate the asymptotic behavior, as time  goes to infinity, of trajectories of second-order evolution equations            () + u ˙ () + (()) + (()) = 0, where is the gradient operator of a convex differentiable potential function : ,: is a maximal monotone operator which is assumed to be-cocoercive, and > 0 is a damping parameter. Potential and non-potential effects are associated...

Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields

Huirong Pi, Chunhua Wang (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we are concerned with the existence of multi-bump solutions for a nonlinear Schrödinger equations with electromagnetic fields. We prove under some suitable conditions that for any positive integer , there exists () > 0 such that, for 0 <  < (), the problem has an -bump complex-valued solution. As a result, when  → 0, the equation has more and more multi-bump complex-valued solutions.

Computing and proving with pivots

Frédéric Meunier (2013)

RAIRO - Operations Research - Recherche Opérationnelle

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A simple idea used in many combinatorial algorithms is the idea of . Originally, it comes from the method proposed by Gauss in the 19th century for solving systems of linear equations. This method had been extended in 1947 by Dantzig for the famous simplex algorithm used for solving linear programs. From since, a pivoting algorithm is a method exploring subsets of a ground set and going from one subset to a new one ′ by deleting an element inside and adding an element outside : ′ =  ...

Analysis of a near-metric TSP approximation algorithm

Sacha Krug (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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The traveling salesman problem (TSP) is one of the most fundamental optimization problems. We consider the -metric traveling salesman problem ( -TSP), , the TSP restricted to graphs satisfying the -triangle inequality ({}) ≤ (({}) + ({})), for some cost function and any three vertices . The well-known path matching Christofides algorithm (PMCA) guarantees an approximation ratio of 3 /2 and is the best known algorithm for the -TSP, for 1 ≤  ≤ 2....

Continuity of solutions of a nonlinear elliptic equation

Pierre Bousquet (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider a nonlinear elliptic equation of the form div [(∇)] + [] = 0 on a domain Ω, subject to a Dirichlet boundary condition tr = . We do not assume that the higher order term satisfies growth conditions from above. We prove the existence of continuous solutions either when Ω is convex and satisfies a one-sided bounded slope condition, or when is radial: a ( ξ ) = l ( | ξ | ) | ξ | ξ a ( ξ ) = l ( | ξ | ) | ξ | ξ for some increasing:ℝ → ℝ

The continuous Coupled Cluster formulation for the electronic Schrödinger equation

Thorsten Rohwedder (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Nowadays, the Coupled Cluster (CC) method is the probably most widely used high precision method for the solution of the main equation of electronic structure calculation, the . Traditionally, the equations of CC are formulated as a nonlinear approximation of a Galerkin solution of the electronic Schrödinger equation, within a given discrete subspace. Unfortunately, this concept prohibits the direct application of concepts of nonlinear numerical analysis to obtain existence and uniqueness...

Some results on complexity of μ-calculus evaluation in the black-box model

Paweł Parys (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We consider -calculus formulas in a normal form: after a prefix of fixed-point quantifiers follows a quantifier-free expression. We are interested in the problem of evaluating (model checking) such formulas in a powerset lattice. We assume that the quantifier-free part of the expression can be any monotone function given by a black-box – we may only ask for its value for given arguments. As a first result we prove that when the lattice is fixed, the problem becomes polynomial (the assumption...

Hereditary properties of words

József Balogh, Béla Bollobás (2010)

RAIRO - Theoretical Informatics and Applications

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Let be a hereditary property of words, , an infinite class of finite words such that every subword (block) of a word belonging to is also in . Extending the classical Morse-Hedlund theorem, we show that either contains at least words of length for every  or, for some , it contains at most words of length for every . More importantly, we prove the following quantitative extension of this result: if has words of length then, for every , it contains at most ⌈( + 1)/2⌉⌈( + 1)/2⌈...