Weak Convergence of a Relaxed and Inertial Hybrid Projection-Proximal Point Algorithm for Maximal Monotone Operators in Hilbert Space

Álvarez, Felipe

doi:10.1137/s1052623403427859

Cited by 267 publications

(155 citation statements)

References 17 publications

Supporting

Mentioning

145

Contrasting

Unclassified

Order By: Relevance

“…In this section, we consider a numerical example in [11] 1 ] are all generated randomly. In the implementations, we take Ax − By < ε = 10 −4 as the stopping criterion.…”

Section: Preliminary Numerical Resultsmentioning

confidence: 99%

Solve the split equality problem by a projection algorithm with inertial effects

Dong¹,

Jiang²

2017

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

show abstract

“…In this section, we consider a numerical example in [11] 1 ] are all generated randomly. In the implementations, we take Ax − By < ε = 10 −4 as the stopping criterion.…”

Section: Preliminary Numerical Resultsmentioning

confidence: 99%

Solve the split equality problem by a projection algorithm with inertial effects

Dong¹,

Jiang²

2017

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

show abstract

“…The following results is a very useful tool in the convergence analysis of inertial algorithms (see [1,2,20]). …”

Section: Lemma 3 Let U ∈ Smentioning

confidence: 99%

An Inertial Proximal-Gradient Penalization Scheme for Constrained Convex Optimization Problems

2017

View full text Add to dashboard Cite

We propose a proximal-gradient algorithm with penalization terms and inertial and memory effects for minimizing the sum of a proper, convex, and lower semicontinuous and a convex differentiable function subject to the set of minimizers of another convex differentiable function. We show that, under suitable choices for the step sizes and the penalization parameters, the generated iterates weakly converge to an optimal solution of the addressed bilevel optimization problem, while the objective function values converge to its optimal objective value.

show abstract

“…The following proposition will play an essential role in the convergence analysis (see also [1][2][3]16]). …”

Section: Lemma 6 Let X ∈ S and Set P := −∇ F (X)mentioning

confidence: 99%

“…The resulting iterative schemes share the feature that the next iterate is defined by means of the last two iterates, a fact which induces the inertial effect in the algorithm. Since the works [1,3], one can notice an increasing number of research efforts dedicated to algorithms of inertial type (see [1][2][3]9,[16][17][18][19][24][25][26][27][28][30][31][32]34]). …”

Section: Introductionmentioning

confidence: 99%

Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data

2017

View full text Add to dashboard Cite

We consider the problem of minimizing a smooth convex objective function subject to the set of minima of another differentiable convex function. In order to solve this problem, we propose an algorithm which combines the gradient method with a penalization technique. Moreover, we insert in our algorithm an inertial term, which is able to take advantage of the history of the iterates. We show weak convergence of the generated sequence of iterates to an optimal solution of the optimization problem, provided a condition expressed via the Fenchel conjugate of the constraint function is fulfilled. We also prove convergence for the objective function values to the optimal objective value. The convergence analysis carried out in this paper relies on the celebrated Opial Lemma and generalized Fejér monotonicity techniques. We illustrate the functionality of the method via a numerical experiment addressing image classification via support vector machines.

show abstract

Weak Convergence of a Relaxed and Inertial Hybrid Projection-Proximal Point Algorithm for Maximal Monotone Operators in Hilbert Space

Cited by 267 publications

References 17 publications

Solve the split equality problem by a projection algorithm with inertial effects

Solve the split equality problem by a projection algorithm with inertial effects

An Inertial Proximal-Gradient Penalization Scheme for Constrained Convex Optimization Problems

Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data

Contact Info

Product

Resources

About