The Experts below are selected from a list of 3687 Experts worldwide ranked by ideXlab platform
Valkonen Tuomo - One of the best experts on this subject based on the ideXlab platform.
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Primal-dual block-proximal splitting for a class of non-convex problems. ETNA - Electronic Transactions on Numerical Analysis
'Osterreichische Akademie der Wissenschaften', 2020Co-Authors: Jauhiainen Jyrki, Mazurenko Stanislav, Valkonen TuomoAbstract:We develop block structure-adapted primal-dual algorithms for non-convexnon-smooth optimisation problems, whose objectives can be written as compositions$G(x)+F(K(x))$ of non-smooth block-separable convex functions $G$ and $F$ with anonlinear Lipschitz-Differentiable Operator $K$. Our methods are refinements ofthe nonlinear primal-dual proximal splitting method for such problems withoutthe block structure, which itself is based on the primal-dual proximal splittingmethod of Chambolle and Pock for convex problems. We propose individual steplength parameters and acceleration rules for each of the primal and dual blocksof the problem. This allows them to convergence faster by adapting to thestructure of the problem. For the squared distance of the iterates to a criticalpoint, we show local $O(1/N)$, $O(1/N^2)$, and linear rates under varyingconditions and choices of the step length parameters. Finally, we demonstrate the performance of the methods for the practical inverseproblems of diffusion tensor imaging and electrical impedance tomography
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PRIMAL-DUAL BLOCK-PROXIMAL SPLITTING FOR A CLASS OF NON-CONVEX PROBLEMS
'Osterreichische Akademie der Wissenschaften', 2020Co-Authors: Mazurenko Stanislav, Jauhiainen Jyrki, Valkonen TuomoAbstract:We develop block structure-adapted primal-dual algorithms for non-convex non-smooth optimisation problems, whose objectives can be written as compositions G(x) + F(K(x)) of non-smooth block-separable convex functions G and F with a nonlinear Lipschitz-Differentiable Operator K. Our methods are refinements of the nonlinear primal-dual proximal splitting method for such problems without the block structure, which itself is based on the primal-dual proximal splitting method of Chambolle and Pock for convex problems. We propose individual step length parameters and acceleration rules for each of the primal and dual blocks of the problem. This allows them to convergence faster by adapting to the structure of the problem. For the squared distance of the iterates to a critical point, we show local O(1/N), O(1/N-2), and linear rates under varying conditions and choices of the step length parameters. Finally, we demonstrate the performance of the methods for the practical inverse problems of diffusion tensor imaging and electrical impedance tomography.Peer reviewe
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Primal-dual block-proximal splitting for a class of non-convex problems
'Osterreichische Akademie der Wissenschaften', 2020Co-Authors: Mazurenko Stanislav, Jauhiainen Jyrki, Valkonen TuomoAbstract:We develop block structure adapted primal-dual algorithms for non-convex non-smooth optimisation problems whose objectives can be written as compositions $G(x)+F(K(x))$ of non-smooth block-separable convex functions $G$ and $F$ with a non-linear Lipschitz-Differentiable Operator $K$. Our methods are refinements of the non-linear primal-dual proximal splitting method for such problems without the block structure, which itself is based on the primal-dual proximal splitting method of Chambolle and Pock for convex problems. We propose individual step length parameters and acceleration rules for each of the primal and dual blocks of the problem. This allows them to convergence faster by adapting to the structure of the problem. For the squared distance of the iterates to a critical point, we show local $O(1/N)$, $O(1/N^2)$ and linear rates under varying conditions and choices of the step lengths parameters. Finally, we demonstrate the performance of the methods on practical inverse problems: diffusion tensor imaging and electrical impedance tomography
Ioannis K Argyros - One of the best experts on this subject based on the ideXlab platform.
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ball convergence of newton s method for generalized equations using restricted convergence domains and majorant conditions
Nonlinear functional analysis and applications, 2017Co-Authors: Ioannis K Argyros, Santhosh GeorgeAbstract:In this study, we consider Newton’s method for solving the generalized equation of the form F ( x ) + T ( x ) ∋ 0 , in Hilbert space, where F is a Fŕechet Differentiable Operator and T is a set valued and maximal monotone. Using restricted convergence domains and Banach Perturbation lemma we prove the convergence of the method with the following advantages: tighter error estimates on the distances involved and the information on the location of the solution is at least as precise. These advantages were obtained under the same computational cost but using more precise majorant functions.
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improved robust semi local convergence analysis of newton s method for cone inclusion problem in banach spaces under restricted convergence domains and majorant conditions
Nonlinear functional analysis and applications, 2017Co-Authors: Ioannis K Argyros, P Jidesh, Santhosh GeorgeAbstract:In this study, we consider Newton’s method for solving the nonlinear inclusion problems in Banach space, where F is a Fr echet Differentiable Operator. Using restricted convergence domains we prove the convergence of the method with the following advantages: tighter error estimates on the distances involved and the information on the location of the solution is at least as precise. These advantages were obtained under the same computational cost using the idea of restricted convergence domains.
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a unifying local semilocal convergence analysis and applications for two point newton like methods in banach space
Journal of Mathematical Analysis and Applications, 2004Co-Authors: Ioannis K ArgyrosAbstract:Abstract We provide a local as well as a semilocal convergence analysis for two-point Newton-like methods in a Banach space setting under very general Lipschitz type conditions. Our equation contains a Frechet Differentiable Operator F and another Operator G whose differentiability is not assumed. Using more precise majorizing sequences than before we provide sufficient convergence conditions for Newton-like methods to a locally unique solution of equation F(x)+G(x)=0. In the semilocal case we show under weaker conditions that our error estimates on the distances involved are finer and the information on the location of the solution at least as precise as in earlier results. In the local case a larger radius of convergence is obtained. Several numerical examples are provided to show that our results compare favorably with earlier ones. As a special case we show that the famous Newton–Kantorovich hypothesis is weakened under the same hypotheses as the ones contained in the Newton–Kantorovich theorem.
Mazurenko Stanislav - One of the best experts on this subject based on the ideXlab platform.
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Primal-dual block-proximal splitting for a class of non-convex problems. ETNA - Electronic Transactions on Numerical Analysis
'Osterreichische Akademie der Wissenschaften', 2020Co-Authors: Jauhiainen Jyrki, Mazurenko Stanislav, Valkonen TuomoAbstract:We develop block structure-adapted primal-dual algorithms for non-convexnon-smooth optimisation problems, whose objectives can be written as compositions$G(x)+F(K(x))$ of non-smooth block-separable convex functions $G$ and $F$ with anonlinear Lipschitz-Differentiable Operator $K$. Our methods are refinements ofthe nonlinear primal-dual proximal splitting method for such problems withoutthe block structure, which itself is based on the primal-dual proximal splittingmethod of Chambolle and Pock for convex problems. We propose individual steplength parameters and acceleration rules for each of the primal and dual blocksof the problem. This allows them to convergence faster by adapting to thestructure of the problem. For the squared distance of the iterates to a criticalpoint, we show local $O(1/N)$, $O(1/N^2)$, and linear rates under varyingconditions and choices of the step length parameters. Finally, we demonstrate the performance of the methods for the practical inverseproblems of diffusion tensor imaging and electrical impedance tomography
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PRIMAL-DUAL BLOCK-PROXIMAL SPLITTING FOR A CLASS OF NON-CONVEX PROBLEMS
'Osterreichische Akademie der Wissenschaften', 2020Co-Authors: Mazurenko Stanislav, Jauhiainen Jyrki, Valkonen TuomoAbstract:We develop block structure-adapted primal-dual algorithms for non-convex non-smooth optimisation problems, whose objectives can be written as compositions G(x) + F(K(x)) of non-smooth block-separable convex functions G and F with a nonlinear Lipschitz-Differentiable Operator K. Our methods are refinements of the nonlinear primal-dual proximal splitting method for such problems without the block structure, which itself is based on the primal-dual proximal splitting method of Chambolle and Pock for convex problems. We propose individual step length parameters and acceleration rules for each of the primal and dual blocks of the problem. This allows them to convergence faster by adapting to the structure of the problem. For the squared distance of the iterates to a critical point, we show local O(1/N), O(1/N-2), and linear rates under varying conditions and choices of the step length parameters. Finally, we demonstrate the performance of the methods for the practical inverse problems of diffusion tensor imaging and electrical impedance tomography.Peer reviewe
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Primal-dual block-proximal splitting for a class of non-convex problems
'Osterreichische Akademie der Wissenschaften', 2020Co-Authors: Mazurenko Stanislav, Jauhiainen Jyrki, Valkonen TuomoAbstract:We develop block structure adapted primal-dual algorithms for non-convex non-smooth optimisation problems whose objectives can be written as compositions $G(x)+F(K(x))$ of non-smooth block-separable convex functions $G$ and $F$ with a non-linear Lipschitz-Differentiable Operator $K$. Our methods are refinements of the non-linear primal-dual proximal splitting method for such problems without the block structure, which itself is based on the primal-dual proximal splitting method of Chambolle and Pock for convex problems. We propose individual step length parameters and acceleration rules for each of the primal and dual blocks of the problem. This allows them to convergence faster by adapting to the structure of the problem. For the squared distance of the iterates to a critical point, we show local $O(1/N)$, $O(1/N^2)$ and linear rates under varying conditions and choices of the step lengths parameters. Finally, we demonstrate the performance of the methods on practical inverse problems: diffusion tensor imaging and electrical impedance tomography
Argyros, Ioannis K. - One of the best experts on this subject based on the ideXlab platform.
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King-Werner-type methods of order 1 + √2
'Informa UK Limited', 2020Co-Authors: Argyros, Ioannis K., Magreñán, Á. AlbertoAbstract:Capítulo del libro "Iterative Methods and Their Dynamics with Applications"Iterative methods are used to generate a sequence of approximating a solution x of the nonlinear equation F(x) = 0, (10.1) where F is Fréchet-Differentiable Operator defined on a convex subset D of a Banach space X with values in a Banach space Y
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Secant-like methods
'Informa UK Limited', 2020Co-Authors: Argyros, Ioannis K., Magreñán, Á. AlbertoAbstract:Capítulo del libro "Iterative Methods and Their Dynamics with Applications"In this chapter we study the problem of finding a locally unique solution x of equation F(x) = 0, (13.1) where F is a Fréchet-Differentiable Operator defined on a convex subset D of a Banach space χ with values in a Banach space Y
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A unifying local–semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
Elsevier Inc., 2004Co-Authors: Argyros, Ioannis K.Abstract:AbstractWe provide a local as well as a semilocal convergence analysis for two-point Newton-like methods in a Banach space setting under very general Lipschitz type conditions. Our equation contains a Fréchet Differentiable Operator F and another Operator G whose differentiability is not assumed. Using more precise majorizing sequences than before we provide sufficient convergence conditions for Newton-like methods to a locally unique solution of equation F(x)+G(x)=0. In the semilocal case we show under weaker conditions that our error estimates on the distances involved are finer and the information on the location of the solution at least as precise as in earlier results. In the local case a larger radius of convergence is obtained. Several numerical examples are provided to show that our results compare favorably with earlier ones. As a special case we show that the famous Newton–Kantorovich hypothesis is weakened under the same hypotheses as the ones contained in the Newton–Kantorovich theorem
Jauhiainen Jyrki - One of the best experts on this subject based on the ideXlab platform.
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Primal-dual block-proximal splitting for a class of non-convex problems. ETNA - Electronic Transactions on Numerical Analysis
'Osterreichische Akademie der Wissenschaften', 2020Co-Authors: Jauhiainen Jyrki, Mazurenko Stanislav, Valkonen TuomoAbstract:We develop block structure-adapted primal-dual algorithms for non-convexnon-smooth optimisation problems, whose objectives can be written as compositions$G(x)+F(K(x))$ of non-smooth block-separable convex functions $G$ and $F$ with anonlinear Lipschitz-Differentiable Operator $K$. Our methods are refinements ofthe nonlinear primal-dual proximal splitting method for such problems withoutthe block structure, which itself is based on the primal-dual proximal splittingmethod of Chambolle and Pock for convex problems. We propose individual steplength parameters and acceleration rules for each of the primal and dual blocksof the problem. This allows them to convergence faster by adapting to thestructure of the problem. For the squared distance of the iterates to a criticalpoint, we show local $O(1/N)$, $O(1/N^2)$, and linear rates under varyingconditions and choices of the step length parameters. Finally, we demonstrate the performance of the methods for the practical inverseproblems of diffusion tensor imaging and electrical impedance tomography
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PRIMAL-DUAL BLOCK-PROXIMAL SPLITTING FOR A CLASS OF NON-CONVEX PROBLEMS
'Osterreichische Akademie der Wissenschaften', 2020Co-Authors: Mazurenko Stanislav, Jauhiainen Jyrki, Valkonen TuomoAbstract:We develop block structure-adapted primal-dual algorithms for non-convex non-smooth optimisation problems, whose objectives can be written as compositions G(x) + F(K(x)) of non-smooth block-separable convex functions G and F with a nonlinear Lipschitz-Differentiable Operator K. Our methods are refinements of the nonlinear primal-dual proximal splitting method for such problems without the block structure, which itself is based on the primal-dual proximal splitting method of Chambolle and Pock for convex problems. We propose individual step length parameters and acceleration rules for each of the primal and dual blocks of the problem. This allows them to convergence faster by adapting to the structure of the problem. For the squared distance of the iterates to a critical point, we show local O(1/N), O(1/N-2), and linear rates under varying conditions and choices of the step length parameters. Finally, we demonstrate the performance of the methods for the practical inverse problems of diffusion tensor imaging and electrical impedance tomography.Peer reviewe
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Primal-dual block-proximal splitting for a class of non-convex problems
'Osterreichische Akademie der Wissenschaften', 2020Co-Authors: Mazurenko Stanislav, Jauhiainen Jyrki, Valkonen TuomoAbstract:We develop block structure adapted primal-dual algorithms for non-convex non-smooth optimisation problems whose objectives can be written as compositions $G(x)+F(K(x))$ of non-smooth block-separable convex functions $G$ and $F$ with a non-linear Lipschitz-Differentiable Operator $K$. Our methods are refinements of the non-linear primal-dual proximal splitting method for such problems without the block structure, which itself is based on the primal-dual proximal splitting method of Chambolle and Pock for convex problems. We propose individual step length parameters and acceleration rules for each of the primal and dual blocks of the problem. This allows them to convergence faster by adapting to the structure of the problem. For the squared distance of the iterates to a critical point, we show local $O(1/N)$, $O(1/N^2)$ and linear rates under varying conditions and choices of the step lengths parameters. Finally, we demonstrate the performance of the methods on practical inverse problems: diffusion tensor imaging and electrical impedance tomography