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Article Dans Une Revue Journal of Global Optimization Année : 2021

Global Convergence of Model Function Based Bregman Proximal Minimization Algorithms

Résumé

Lipschitz continuity of the gradient mapping of a continuously differentiable function plays a crucial role in designing various optimization algorithms. However, many functions arising in practical applications such as low rank matrix factorization or deep neural network problems do not have a Lipschitz continuous gradient. This led to the development of a generalized notion known as the Lsmad property, which is based on generalized proximity measures called Bregman distances. However, the L-smad property cannot handle nonsmooth functions, for example, simple nonsmooth functions like |x^4 − 1| and also many practical composite problems are out of scope. We fix this issue by proposing the MAP property, which generalizes the L-smad property and is also valid for a large class of structured nonconvex nonsmooth composite problems. Based on the proposed MAP property, we propose a globally convergent algorithm called Model BPG, that unifies several existing algorithms. The convergence analysis is based on a new Lyapunov function. We also numerically illustrate the superior performance of Model BPG on standard phase retrieval problems and Poisson linear inverse problems, when compared to a state of the art optimization method that is valid for generic nonconvex nonsmooth optimization problems.
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Dates et versions

hal-03452326 , version 1 (26-11-2021)

Identifiants

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Mahesh Chandra Mukkamala, Jalal M. Fadili, Peter Ochs. Global Convergence of Model Function Based Bregman Proximal Minimization Algorithms. Journal of Global Optimization, In press, 83 (4), pp.753-781. ⟨10.1007/s10898-021-01114-y⟩. ⟨hal-03452326⟩
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