Optimization of upper semidifferentiable functions

Bihain, Anderson Luis Jeske

doi:10.1007/bf00938396

Cited by 46 publications

(16 citation statements)

References 10 publications

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“…Let I = f1 : : : N +2g. F rom g k 2 @f(y k ), k 1, Lemma 3 and Caratheodory's 2 =u T k v k and the rst part of (3.5) follows from the rst part of (2.9). Furthermore, (2.10) implies T r (H k+1 ) = T r (H k ) + %N ; j v k j 2 =u T k v k and the second part of (3.5) follows from the second part of (2.9).…”

Section: Derivation Of the Methodsmentioning

confidence: 99%

Globally Convergent Variable Metric Method for Nonconvex Nondifferentiable Unconstrained Minimization

Vlček

Lukšan

2001

Journal of Optimization Theory and Applications

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Section: Derivation Of the Methodsmentioning

confidence: 99%

Globally Convergent Variable Metric Method for Nonconvex Nondifferentiable Unconstrained Minimization

Vlček

Lukšan

2001

Journal of Optimization Theory and Applications

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“…Under the upper semismoothness assumption [47], LMBM can be proved to be globally convergent for locally Lipschitz continuous objective functions [35,37].…”

Section: Limited Memory Bundle Methodsmentioning

confidence: 99%

Diagonal Bundle Method for Nonsmooth Sparse Optimization

Karmitsa

2014

J Optim Theory Appl

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We propose an efficient diagonal bundle method for sparse nonsmooth, possibly nonconvex optimization. The convergence of the proposed method is proved for locally Lipschitz continuous functions, which are not necessary differentiable or convex. The numerical experiments have been made using problems with up to million variables. The results to be presented confirm the usability of the diagonal bundle method especially for extremely large-scale problems.

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“…On the other hand, the purely quadratic, smooth formulation, min u Z 1 2 ju ? zj 2 dx + g Z 1 2 jruj 2 dx; (2) recovers smooth surfaces well, but smears out sharp edges of the image. In order to generalize the above approaches, we study the following optimization problem 4]…”

Section: Introductionmentioning

confidence: 91%

Comparison of formulations and solution methods for image restoration problems

Kärkkäinen¹,

Majava²,

Mäkelä³

2001

Inverse Problems

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The purpose of this paper is twofold: First aim is to seek for a proper formulation for recovering both sharp edges and smooth surfaces from a given, noisy, image. The formulations proposed here can be di erentiable, but as our numerical experiments show, so close to a nonsmooth problem that ordinary optimization methods for smooth problems, like the conjugate gradient method, have di culties in convergence. Hence, another aim of this paper is to compare di erent numerical methods for solving the image restoration problems. Two methods of nonsmooth optimization are applied: a (rst order) proximal bundle method and a (second order) bundle-Newton method. Moreover, a generalization of the active-set methods that have earlier shown high e ciency for nonsmooth image restoration problems is proposed and analysed. Comparison of the methods as well as comparison of formulations are made through numerical experiments.

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Optimization of upper semidifferentiable functions

Cited by 46 publications

References 10 publications

Globally Convergent Variable Metric Method for Nonconvex Nondifferentiable Unconstrained Minimization

Globally Convergent Variable Metric Method for Nonconvex Nondifferentiable Unconstrained Minimization

Diagonal Bundle Method for Nonsmooth Sparse Optimization

Comparison of formulations and solution methods for image restoration problems

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