We present a review of the classical proximal point method for nding zeroes of maximal monotone operators, and its application to augmented Lagrangian methods, including a rather complete convergence analysis. Next we discuss the generalized proximal point methods, either with Bregman distances or -divergences, which in turn give raise to a family of generalized augmented Lagrangians, as smooth...

The oil and gas networks are overlapped because of the inclusion associated in crude oil. This necessitates integration planning supply chain together. In recent years, hydrocarbon market has experienced high fluctuation demands prices which leads to considerable economic disruptions. Therefore, chain, considering uncertainty is a significant area research. this regard, study develops multi-obj...

Multi-objective combinatorial optimization (MOCO) problems, apart from being notoriously difficult and complex to solve in reasonable computational time, they also exhibit high levels of instability in their results in case of uncertainty, which often deviate far from optimality. In this work we propose an integrated methodology to measure and analyze the robustness of MOCO problems, and more s...

We propose explicit K-symplectic and symplectic-like methods for the charged particle system in a general strong magnetic field. The are also symmetric. can be expressed both canonical non-canonical Hamiltonian system. If three components of field integrated closed forms, we construct system; otherwise, constructed by extending original phase space obtaining augmented separable Hamiltonian, the...

We consider a one-dimensional variational problem arising in connection with model for cholesteric liquid crystals. The principal feature of our study is the assumption that twist deformation nematic director incurs much higher energy penalty than other modes deformation. appropriate ratio elastic constants then gives small parameter ε entering an Allen-Cahn-type functional augmented by term. b...

In this paper, we improve a result by Arora, Khot, Kolla, Steurer, Tulsiani, and Vishnoi on solving the Unique Games problem on expanders. Given a (1−ε)-satisfiable instance of Unique Games with the constraint graph G, our algorithm finds an assignment satisfying at least a 1 − Cε/hG fraction of all constraints if ε < cλG where hG is the edge expansion of G, λG is the second smallest eigenvalue...

We present a new particle tracking algorithm for accurately resolving large deformation and rotational motion fields, which takes advantage of both local global algorithms. call this method ScalE Rotation Invariant Augmented Lagrangian Particle Tracking (SerialTrack). This builds an iterative scale rotation invariant topology-based feature vector each within multi-scale algorithm. The kinematic...

A nite element formulation to deal with the friction contact problem between an elastic body and a rigid foundation is presented. An augmented Lagrangian method, which incorporates two Lagrange multipliers and a slack variable in the constraint equation, is developed. In this method, the solution is achieved through a Newton-Raphson monolithic iterative strategy and leads to simple implementati...

We investigate risk-averse stochastic optimization problems where riskaverse preferences are modeled with a stochastic order constraint. We propose augmented Lagrangian methods for the numerical solution of problems with multivariate and univariate stochastic order relations. The methods constructs finite-dimensional approximations of the optimization problem whose solutions converge to the sol...

A numerical method for the computation of the best constant in a Sobolev inequality involving the spacesH2(Ω) and C0(Ω) is presented. Green’s functions corresponding to the solution of Poisson problems are used to express the solution. This (kind of) non-smooth eigenvalue problem is then formulated as a constrained optimization problem and solved with two different strategies: an augmented Lagr...