Yassine Nabou
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Yassine Nabou has a total of 2 co-authors. Here are the top co-authors by number of shared publications:
- Ion Necoara
Automatic Control and Systems Engineering Department, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania; and Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania
5 shared publications - François Glineur
UCLouvain
2 shared publications
Latest Publications
- Open Access
Regularized higher-order Taylor approximation methods for nonlinear least-squares
In this paper, we develop a regularized higher-order Taylor based method for solving composite (e.g., nonlinear least-squares) problems. At each iteration, we replace each smooth component of the objective function by a higher-order Taylor approximation with an appropriate regularization, leading to a regularized higher-order Taylor approximation (RHOTA) algorithm. We derive global convergence guarantees for RHOTA algorithm. In particular, we prove stationary point convergence guarantees for the iterates generated by RHOTA, and leveraging a Kurdyka-Łojasiewicz (KL) type property of the objective function, we derive improved rates depending on the KL parameter. When the Taylor approximation is of order $2$, we present an efficient implementation of RHOTA algorithm, demonstrating that the resulting nonconvex subproblem can be effectively solved utilizing standard convex programming tools. Furthermore, we extend the scope of our investigation to include the behavior and efficacy of RHOTA algorithm in handling systems of nonlinear equations and optimization problems with nonlinear equality constraints deriving new rates under improved constraint qualifications conditions. Finally, we consider solving the phase retrieval problem with a higher-order proximal point algorithm, showcasing its rapid convergence rate for this particular application. Numerical simulations on phase retrieval and output feedback control problems also demonstrate the efficacy and performance of the proposed methods when compared to some state-of-the-art optimization methods and software.Open AccessRegularized higher-order Taylor approximation methods for nonlinear least-squares
In this paper, we develop a regularized higher-order Taylor based method for solving composite (e.g., nonlinear least-squares) problems. At each iteration, we replace each smooth component of the objective function by a higher-order Taylor approximation with an appropriate regularization, leading to a regularized higher-order Taylor approximation (RHOTA) algorithm. We derive global convergence guarantees for RHOTA algorithm. In particular, we prove stationary point convergence guarantees for the iterates generated by RHOTA, and leveraging a Kurdyka-Łojasiewicz (KL) type property of the objective function, we derive improved rates depending on the KL parameter. When the Taylor approximation is of order $2$, we present an efficient implementation of RHOTA algorithm, demonstrating that the resulting nonconvex subproblem can be effectively solved utilizing standard convex programming tools. Furthermore, we extend the scope of our investigation to include the behavior and efficacy of RHOTA algorithm in handling systems of nonlinear equations and optimization problems with nonlinear equality constraints deriving new rates under improved constraint qualifications conditions. Finally, we consider solving the phase retrieval problem with a higher-order proximal point algorithm, showcasing its rapid convergence rate for this particular application. Numerical simulations on phase retrieval and output feedback control problems also demonstrate the efficacy and performance of the proposed methods when compared to some state-of-the-art optimization methods and software. - Open Access
- 30 April 2024
- Published by Springer Nature in Optimization Letters
- Vol. 19 (2) , 285-306
Proximal gradient methods with inexact oracle of degree q for composite optimization
We introduce the concept of inexact first-order oracle of degree q for a possibly nonconvex and nonsmooth function, which naturally appears in the context of approximate gradient, weak level of smoothness and other situations. Our definition is less conservative than those found in the existing literature, and it can be viewed as an interpolation between fully exact and the existing inexact first-order oracle definitions. We analyze the convergence behavior of a (fast) inexact proximal gradient method using such an oracle for solving (non)convex composite minimization problems. We derive complexity estimates and study the dependence between the accuracy of the oracle and the desired accuracy of the gradient or of the objective function. Our results show that better rates can be obtained both theoretically and in numerical simulations when q is large.
- 30 April 2024
- Published by Springer Nature in Optimization Letters
- Vol. 19 (2) , 285-306
Open AccessProximal gradient methods with inexact oracle of degree q for composite optimization
We introduce the concept of inexact first-order oracle of degree q for a possibly nonconvex and nonsmooth function, which naturally appears in the context of approximate gradient, weak level of smoothness and other situations. Our definition is less conservative than those found in the existing literature, and it can be viewed as an interpolation between fully exact and the existing inexact first-order oracle definitions. We analyze the convergence behavior of a (fast) inexact proximal gradient method using such an oracle for solving (non)convex composite minimization problems. We derive complexity estimates and study the dependence between the accuracy of the oracle and the desired accuracy of the gradient or of the objective function. Our results show that better rates can be obtained both theoretically and in numerical simulations when q is large.
- Open Access
Proximal gradient methods with inexact oracle of degree q for composite optimization
We introduce the concept of inexact first-order oracle of degree q for a possibly nonconvex and nonsmooth function, which naturally appears in the context of approximate gradient, weak level of smoothness and other situations. Our definition is less conservative than those found in the existing literature, and it can be viewed as an interpolation between fully exact and the existing inexact first-order oracle definitions. We analyze the convergence behavior of a (fast) inexact proximal gradient method using such an oracle for solving (non)convex composite minimization problems. We derive complexity estimates and study the dependence between the accuracy of the oracle and the desired accuracy of the gradient or of the objective function. Our results show that better rates can be obtained both theoretically and in numerical simulations when q is large.
Open AccessProximal gradient methods with inexact oracle of degree q for composite optimization
We introduce the concept of inexact first-order oracle of degree q for a possibly nonconvex and nonsmooth function, which naturally appears in the context of approximate gradient, weak level of smoothness and other situations. Our definition is less conservative than those found in the existing literature, and it can be viewed as an interpolation between fully exact and the existing inexact first-order oracle definitions. We analyze the convergence behavior of a (fast) inexact proximal gradient method using such an oracle for solving (non)convex composite minimization problems. We derive complexity estimates and study the dependence between the accuracy of the oracle and the desired accuracy of the gradient or of the objective function. Our results show that better rates can be obtained both theoretically and in numerical simulations when q is large.
- Open Access
Efficiency of higher-order algorithms for minimizing composite functions
Composite minimization involves a collection of functions which are aggregated in a nonsmooth manner. It covers, as a particular case, smooth approximation of minimax games, minimization of max-type functions, and simple composite minimization problems, where the objective function has a nonsmooth component. We design a higher-order majorization algorithmic framework for fully composite problems (possibly nonconvex). Our framework replaces each component with a higher-order surrogate such that the corresponding error function has a higher-order Lipschitz continuous derivative. We present convergence guarantees for our method for composite optimization problems with (non)convex and (non)smooth objective function. In particular, we prove stationary point convergence guarantees for general nonconvex (possibly nonsmooth) problems and under Kurdyka-Lojasiewicz (KL) property of the objective function we derive improved rates depending on the KL parameter. For convex (possibly nonsmooth) problems we also provide sublinear convergence rates.
Open AccessEfficiency of higher-order algorithms for minimizing composite functions
Composite minimization involves a collection of functions which are aggregated in a nonsmooth manner. It covers, as a particular case, smooth approximation of minimax games, minimization of max-type functions, and simple composite minimization problems, where the objective function has a nonsmooth component. We design a higher-order majorization algorithmic framework for fully composite problems (possibly nonconvex). Our framework replaces each component with a higher-order surrogate such that the corresponding error function has a higher-order Lipschitz continuous derivative. We present convergence guarantees for our method for composite optimization problems with (non)convex and (non)smooth objective function. In particular, we prove stationary point convergence guarantees for general nonconvex (possibly nonsmooth) problems and under Kurdyka-Lojasiewicz (KL) property of the objective function we derive improved rates depending on the KL parameter. For convex (possibly nonsmooth) problems we also provide sublinear convergence rates.
- 10 October 2023
- Published by Springer Nature in Computational Optimization and Applications
- Vol. 87 (2) , 441-473
Efficiency of higher-order algorithms for minimizing composite functions
- 10 October 2023
- Published by Springer Nature in Computational Optimization and Applications
- Vol. 87 (2) , 441-473
Efficiency of higher-order algorithms for minimizing composite functions