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

Boţ, Radu Ioan; Csetnek, Ernö Robert; Nimana, Nimit

doi:10.1007/s10013-017-0256-9

Cited by 10 publications

(11 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The problem (17) has been considered by many authors, for instance [2,[27][28][29][30] and references therein.…”

Section: Convex Minimization With Complex Constraintsmentioning

confidence: 99%

A Fixed-Point Subgradient Splitting Method for Solving Constrained Convex Optimization Problems

Nimana

2020

Symmetry

Self Cite

View full text Add to dashboard Cite

In this work, we consider a bilevel optimization problem consisting of the minimizing sum of two convex functions in which one of them is a composition of a convex function and a nonzero linear transformation subject to the set of all feasible points represented in the form of common fixed-point sets of nonlinear operators. To find an optimal solution to the problem, we present a fixed-point subgradient splitting method and analyze convergence properties of the proposed method provided that some additional assumptions are imposed. We investigate the solving of some well known problems by using the proposed method. Finally, we present some numerical experiments for showing the effectiveness of the obtained theoretical result.

show abstract

“…The problem (17) has been considered by many authors, for instance [2,[27][28][29][30] and references therein.…”

Section: Convex Minimization With Complex Constraintsmentioning

confidence: 99%

A Fixed-Point Subgradient Splitting Method for Solving Constrained Convex Optimization Problems

Nimana

2020

Symmetry

Self Cite

View full text Add to dashboard Cite

show abstract

“…It is also well known that iterative methods with inertial effects may lead to a considerable improvement of the convergence behavior of the method. We refer the reader to [4,11,[14][15][16]24] and the references therein for more insight into this research topic. Of course, one way to address this research direction is to consider the inertial effects of the proposed algorithms and to analyze their convergence results.…”

Section: Hierarchical Minimization Problemmentioning

confidence: 99%

“…Another approach to motivate problem (2) in the context of nonautonomous multiscaled differential inclusion is due to [1]. We refer the reader to [2,3,13,14,18,23,27] for a rich literature devoted to problem (2). Assume that the solution set of the problem (2) is nonempty and some qualification conditions hold, for instance,…”

Section: Introductionmentioning

confidence: 99%

Generalized forward–backward splitting with penalization for monotone inclusion problems

Nimana

Petrot

2018

J Glob Optim

Self Cite

View full text Add to dashboard Cite

We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another maximally monotone operator. We show weak ergodic convergence of the generated sequence of iterates to a solution of the considered monotone inclusion problem, provided that the condition corresponding to the Fitzpatrick function of the operator describing the set of the normal cone is fulfilled. Under strong monotonicity of an operator, we show strong convergence of the iterates. Furthermore, we utilize the proposed method for minimizing a largescale hierarchical minimization problem concerning the sum of differentiable and nondifferentiable convex functions subject to the set of minima of another differentiable convex function. We illustrate the functionality of the method through numerical experiments addressing constrained elastic net and generalized Heron location problems.Keywords Monotone operator · monotone inclusion · hierarchical optimization · forward-backward algorithm Mathematics Subject Classification (2010) 47H05 · 65K05 · 65K10 · 90C25

show abstract

“…The problem is also called the leader's and follower's problem where the problem (5) is called the leader's problem and (6) is called the follower's problem, meaning, the first player (which is called the leader) makes his selection first and communicates it to the second player (the so-called follower). There are many studies for several type bilevel problems, see, for example, [15,[17][18][19][20][21][22][23][24]. The bilevel optimization problem is a bilevel problem when the hierarchical structure involves the optimization problem.…”

Section: Introductionmentioning

confidence: 99%

Proximal Gradient Method for Solving Bilevel Optimization Problems

Yimer

Gebrie

2020

MCA

View full text Add to dashboard Cite

In this paper, we consider a bilevel optimization problem as a task of finding the optimum of the upper-level problem subject to the solution set of the split feasibility problem of fixed point problems and optimization problems. Based on proximal and gradient methods, we propose a strongly convergent iterative algorithm with an inertia effect solving the bilevel optimization problem under our consideration. Furthermore, we present a numerical example of our algorithm to illustrate its applicability.

show abstract

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

Cited by 10 publications

References 42 publications

A Fixed-Point Subgradient Splitting Method for Solving Constrained Convex Optimization Problems

A Fixed-Point Subgradient Splitting Method for Solving Constrained Convex Optimization Problems

Generalized forward–backward splitting with penalization for monotone inclusion problems

Proximal Gradient Method for Solving Bilevel Optimization Problems

Contact Info

Product

Resources

About