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Journal of optimization theory and applications, ISSN 1573-2878, 2018, Volume 182, Issue 1, pp. 110 - 132
... for Two-Block Separable Convex Optimization Problems with Linear Constraints Sandy Bitterlich1 · Radu Ioan Boţ2 · Ernö Robert Csetnek2,3 · Gert Wanka1 Received: 1... 
Fenchel duality | Lagrangian | Convex optimization | Saddle points | Subdifferential | Proximal AMA | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Image processing | Algorithms | Machine learning | Operators (mathematics) | Computational geometry | Mathematical analysis | Hilbert space | Convexity | Iterative methods | Optimization | Mathematical programming | 65K05 | 90C25 | 47H05
Journal Article
Applied Mathematics & Optimization, ISSN 0095-4616, 12/2019, Volume 80, Issue 3, pp. 665 - 678
Journal Article
Optimization, ISSN 1029-4945, 2018, Volume 68, Issue 7, pp. 1265 - 1277
We consider the minimization of a convex objective function subject to the set of minima of another convex function, under the assumption that both functions... 
convex optimization | Lyapunov analysis | Dynamical systems | nonautonomous systems | Newton dynamics | MATHEMATICS, APPLIED | MAXIMAL MONOTONE-OPERATORS | EQUATIONS | ASYMPTOTIC-BEHAVIOR | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PENALIZATION | OPTIMIZATION | FORWARD-BACKWARD | CONVEX MINIMIZATION | SCHEMES | Damping | Trajectories | Optimization | Differential equations | Convergence
Journal Article
EURO journal on computational optimization, ISSN 2192-4414, 2015, Volume 4, Issue 1, pp. 3 - 25
Journal Article
Journal of dynamics and differential equations, ISSN 1572-9222, 2015, Volume 29, Issue 1, pp. 155 - 168
Journal Article
Vietnam Journal of Mathematics, ISSN 2305-221X, 3/2018, Volume 46, Issue 1, pp. 53 - 71
... Radu Ioan Bot ¸ 1 · Ern¨ o Robert Csetnek 1 · Nimit Nimana 2 Received: 20 March 2017 / Accepted: 24 July 2017 / Published online: 1 September 2017 © The Author... 
65K05 | Penalization | 90C25 | Mathematics, general | Mathematics | Fenchel conjugate | 47H05 | Proximal-gradient algorithm | Inertial algorithm
Journal Article
Set-Valued and Variational Analysis, ISSN 1877-0533, 6/2018, Volume 26, Issue 2, pp. 227 - 245
... Systems with Hidden Acceleration and Hessian Driven Damping T erms Radu Ioan Bot ¸ 1 · Ern¨ o Robert Csetnek 1 Received: 4 October 2016 / Accepted: 10 April 2017... 
Limiting subdifferential | Lyapunov analysis | Kurdyka-Łojasiewicz property | Probability Theory and Stochastic Processes | Mathematics | 90C26 | Dynamical systems | 34G25 | 90C30 | Analysis | 65K10 | Nonsmooth optimization | 47J25 | 47H05 | MATHEMATICS, APPLIED | INEQUALITIES | PROXIMAL ALGORITHM | SUM | Kurdyka-Lojasiewicz property | MONOTONE INCLUSIONS | MINIMIZATION | CONVERGENCE | FORWARD-BACKWARD ALGORITHM
Journal Article
Numerical algorithms, ISSN 1572-9265, 2015, Volume 71, Issue 3, pp. 519 - 540
... monotone inclusion problems Radu Ioan Bot ¸ 1 · Ern¨ o Robert Csetnek 1 Received: 30 June 2014 / Accepted: 11 May 2015 / Published online: 4 June 2015 © Springer... 
Primal-dual algorithm | 65K05 | Subdifferential | Numeric Computing | Theory of Computation | Inertial splitting algorithm | Maximally monotone operator | Algorithms | Algebra | Resolvent | Convex optimization | 90C25 | Numerical Analysis | Computer Science | 47H05 | MATHEMATICS, APPLIED | PROXIMAL POINT ALGORITHM | COMPOSITE | CONVERGENCE | MAPPINGS | OPTIMIZATION | OPERATORS | Operators | Splitting | Image processing | Inertial | Inclusions | Optimization | Convergence
Journal Article
SIAM JOURNAL ON OPTIMIZATION, ISSN 1052-6234, 2019, Volume 29, Issue 2, pp. 1300 - 1328
We propose a proximal algorithm for minimizing objective functions consisting of three summands: the composition of a nonsmooth function with a linear... 
limiting subdifferential | MATHEMATICS, APPLIED | full splitting scheme | proximal algorithm | structured nonconvex and nonsmooth optimization | CONVERGENCE | Kurdyka-Lojasiewicz property | POINTS | ALTERNATING LINEARIZED MINIMIZATION
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2016, Volume 435, Issue 2, pp. 1688 - 1700
We investigate the existence and uniqueness of (locally) absolutely continuous trajectories of a penalty term-based dynamical system associated to a... 
Lyapunov analysis | Penalty schemes | Monotone inclusions | Dynamical systems | Forward–backward algorithm | Forward-backward algorithm | HILBERT-SPACES | MATHEMATICS, APPLIED | MATHEMATICS | MONOTONE INCLUSION PROBLEMS | PENALIZATION | FORWARD-BACKWARD | CONVEX MINIMIZATION | SCHEMES
Journal Article
Analysis and Applications, ISSN 0219-5305, 09/2018, Volume 16, Issue 5, pp. 601 - 622
In this paper, we investigate in a Hilbert space setting a second-order dynamical system of the form <(x)double over dot>(t) + gamma(t)<(x)over dot>(t) + x(t)... 
monotone inclusions | Lyapunov analysis | Dynamical systems | penalty schemes | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | OPTIMIZATION | FORWARD-BACKWARD | PENALIZATION SCHEME
Journal Article
Numerical functional analysis and optimization, ISSN 1532-2467, 2015, Volume 36, Issue 8, pp. 951 - 963
Journal Article
Vietnam Journal of Mathematics, ISSN 2305-221X, 12/2014, Volume 42, Issue 4, pp. 451 - 465
... and Parallel-Sum Type Monotone Operators Radu Ioan Bo¸ t · Ernö Robert Csetnek Received: 1 August 2013 / Accepted: 25 September 2013 / Published online: 30 October 2013... 
65K05 | Fitzpatrick function | Infimal-convolution | Subdifferential | Convex minimization problem | Mathematics | Lipschitz continuous operator | Parallel-sum | Maximally monotone operator | Resolvent | 90C25 | Mathematics, general | Forward–backward–forward algorithm | Fenchel conjugate | 47H05
Journal Article
Set-valued and variational analysis, ISSN 1877-0533, 07/2020
Journal Article
Optimization Letters, ISSN 1862-4472, 1/2018, Volume 12, Issue 1, pp. 17 - 33
... convex optimization problems with smooth data Radu Ioan Bo¸ t 1,2 · Ernö Robert Csetnek 1 · Nimit Nimana 3 Received: 2 September 2016 / Accepted: 2 June 2017... 
Computational Intelligence | Penalization | Operations Research/Decision Theory | Mathematics | Numerical and Computational Physics, Simulation | Fenchel conjugate | Gradient method | Optimization | Inertial algorithm | SCHEME | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | ALGORITHM | CONVERGENCE | Analysis | Methods | Algorithms | Original Paper
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 367, Issue 2, pp. 693 - 698
In this paper we provide some extension results for n-cyclically monotone operators in reflexive Banach spaces by making use of the Fenchel duality. In this... 
Fenchel duality | Debrunner–Flor extension | Cyclic monotonicity | Debrunner-Flor extension | MATHEMATICS | MATHEMATICS, APPLIED | MAXIMAL MONOTONICITY | FITZPATRICK FUNCTIONS | CONSTRAINT QUALIFICATIONS | CONVEX-FUNCTIONS
Journal Article
06/2020
The aim of this survey is to present the main important techniques and tools from variational analysis used for first and second order dynamical systems of... 
Mathematics - Optimization and Control
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 04/2015, Volume 256, pp. 472 - 487
Journal Article
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