Výsledky vyhledávání - "Nadav Hallak"

An Adaptive Lagrangian-Based Scheme for Nonconvex Composite Optimization

Autor: Nadav Hallak, Marc Teboulle

Publikováno v: Mathematics of Operations Research.

This paper develops a novel adaptive, augmented, Lagrangian-based method to address the comprehensive class of nonsmooth, nonconvex models with a nonlinear, functional composite structure in the objective. The proposed method uses an adaptive mechani

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f763fa7b9412ff3683c005176bcafc16
https://doi.org/10.1287/moor.2022.1342

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A Dynamic Alternating Direction of Multipliers for Nonconvex Minimization with Nonlinear Functional Equality Constraints

Autor: Marc Teboulle, Nadav Hallak, Eyal Cohen

Publikováno v: Journal of Optimization Theory and Applications. 193:324-353

This paper studies the minimization of a broad class of nonsmooth nonconvex objective functions subject to nonlinear functional equality constraints, where the gradients of the differentiable parts in the objective and the constraints are only locall

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::55af66571eaccbdfc90d4e15e7a9779b
https://doi.org/10.1007/s10957-021-01929-5

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Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach

Autor: Marc Teboulle, Nadav Hallak

Publikováno v: Journal of Optimization Theory and Applications. 186:480-503

This paper introduces a method for computing points satisfying the second-order necessary optimality conditions for nonconvex minimization problems subject to a closed and convex constraint set. The method comprises two independent steps correspondin

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::2abc1993e640d805cb7d50a1e85dad84
https://doi.org/10.1007/s10957-020-01713-x

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On the Convergence to Stationary Points of Deterministic and Randomized Feasible Descent Directions Methods

Autor: Nadav Hallak, Amir Beck

Publikováno v: SIAM Journal on Optimization. 30:56-79

This paper studies the class of nonsmooth nonconvex problems in which the difference between a continuously differentiable function and a convex nonsmooth function is minimized over linear constrai...

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::13e9bd81c7c7719f01cc504a8cd5263c
https://doi.org/10.1137/18m1217760

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A non-Euclidean gradient descent method with sketching for unconstrained matrix minimization

Autor: Marc Teboulle, Nadav Hallak

Publikováno v: Operations Research Letters. 47:421-426

We propose a method that incorporates a non-Euclidean gradient descent step with a generic matrix sketching procedure, for solving unconstrained, nonconvex, matrix optimization problems, in which the decision variable cannot be saved in memory due to

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::24a64f38dfb990748cac7e0a87dfb85f
https://doi.org/10.1016/j.orl.2019.08.001

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On the almost sure convergence of stochastic gradient descent in non-convex problems

Autor: Mertikopoulos, P., Nadav Hallak, Kavis, A., Cevher, V.

Publikováno v: NeurIPS 2020-34th International Conference on Neural Information Processing Systems
NeurIPS 2020-34th International Conference on Neural Information Processing Systems, Dec 2020, Vancouver, Canada. pp.1-32
Scopus-Elsevier

This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm's convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and converges wit

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a134aebe5ae854b4fe534d2ae62ec9bd
https://hal.inria.fr/hal-03043771/document

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Efficient Proximal Mapping of the 1-path-norm of Shallow Networks

Autor: Latorre, F., Rolland, P., Nadav Hallak, Cevher, V.

Publikováno v: Scopus-Elsevier

We demonstrate two new important properties of the 1-path-norm of shallow neural networks. First, despite its non-smoothness and non-convexity it allows a closed form proximal operator which can be efficiently computed, allowing the use of stochastic

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::13031b07a0cd4b620a07e01787669cd7
http://arxiv.org/abs/2007.01003

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Optimization problems involving group sparsity terms

Autor: Amir Beck, Nadav Hallak

Publikováno v: Mathematical Programming. 178:39-67

This paper studies a general form problem in which a lower bounded continuously differentiable function is minimized over a block separable set incorporating a group sparsity expression as a constraint or a penalty (or both) in the group sparsity set

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::4869eff6f19a51de78d5108a60a0f4c4
https://doi.org/10.1007/s10107-018-1277-1

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Proximal Mapping for Symmetric Penalty and Sparsity

Autor: Amir Beck, Nadav Hallak

Publikováno v: SIAM Journal on Optimization. 28:496-527

This paper studies a class of problems consisting of minimizing a continuously differentiable function penalized with the so-called $\ell_0$-norm over a symmetric set. These problems are hard to solve, yet prominent in many fields and applications. W

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::622a0a54f8c882f15f2a2b7f0d373b4e
https://doi.org/10.1137/17m1116544

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