Dynamics of Dengue epidemics using optimal control [PDF]
, 2010 We present an application of optimal control theory to Dengue epidemics. This epidemiologic disease is an important theme in tropical countries due to the growing number of infected individuals.
Betts +14 more
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Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems [PDF]
, 2013 We consider projection algorithms for solving (nonconvex) feasibility problems in Euclidean spaces. Of special interest are the Method of Alternating Projections (MAP) and the Douglas-Rachford or Averaged Alternating Reflection Algorithm (AAR).
Hesse, Robert, Luke, D. Russell
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Linear Convergence of the Douglas-Rachford Method for Two Closed Sets [PDF]
, 2015 In this paper, we investigate the Douglas-Rachford method for two closed (possibly nonconvex) sets in Euclidean spaces. We show that under certain regularity conditions, the Douglas-Rachford method converges locally with R-linear rate. In convex settings,
Phan, Hung M.
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Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows [PDF]
, 2018 This paper concerns an extension of discrete gradient methods to finite-dimensional Riemannian manifolds termed discrete Riemannian gradients, and their application to dissipative ordinary differential equations.
Celledoni, Elena +3 more
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Derivative-free optimization and filter methods to solve nonlinear constrained problems [PDF]
, 2009 In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives,
Correia, Aldina +3 more
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An interior-point method for mpecs based on strictly feasible relaxations. [PDF]
, 2004 An interior-point method for solving mathematical programs with equilibrium constraints (MPECs) is proposed. At each iteration of the algorithm, a single primaldual step is computed from each subproblem of a sequence.
Angel Víctor De Miguel +4 more
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Tensor Methods for Minimizing Convex Functions with H\"{o}lder Continuous Higher-Order Derivatives
, 2020 In this paper we study $p$-order methods for unconstrained minimization of convex functions that are $p$-times differentiable ($p\geq 2$) with $\nu$-H\"{o}lder continuous $p$th derivatives. We propose tensor schemes with and without acceleration. For the
Grapiglia, Geovani Nunes +1 more
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An augmented lagrangian interior point method using diretions of negative curvature [PDF]
, 2000 We describe an efficient implementation of an interior-point algorithm for non-convex problems that uses directions of negative curvature. These directions should ensure convergence to second-order KKT points and improve the computational efficiency of ...
Moguerza, Javier M. +1 more
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, 2014 In a Hilbert framework, we introduce continuous and discrete dynamical systems which aim at solving inclusions governed by structured monotone operators $A=\partial\Phi+B$, where $\partial\Phi$ is the subdifferential of a convex lower semicontinuous ...
Abbas, Boushra, Attouch, Hedy
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Uniform Convergence of the Newton Method for Aubin Continuous Maps [PDF]
, 1996 * This work was supported by National Science Foundation grant DMS 9404431.In this paper we prove that the Newton method applied to the generalized equation y ∈ f(x) + F(x) with a C^1 function f and a set-valued map F acting in Banach spaces, is locally ...
Dontchev, Asen
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