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A second-order dynamical system with Hessian-driven damping and penalty term associated to variational inequalities
- Source :
- Optimization
- Publication Year :
- 2018
- Publisher :
- Informa UK Limited, 2018.
-
Abstract
- We consider the minimization of a convex objective function subject to the set of minima of another convex function, under the assumption that both functions are twice continuously differentiable. We approach this optimization problem from a continuous perspective by means of a second-order dynamical system with Hessian-driven damping and a penalty term corresponding to the constrained function. By constructing appropriate energy functionals, we prove weak convergence of the trajectories generated by this differential equation to a minimizer of the optimization problem as well as convergence for the objective function values along the trajectories. The performed investigations rely on Lyapunov analysis in combination with the continuous version of the Opial Lemma. In case the objective function is strongly convex, we can even show strong convergence of the trajectories.
- Subjects :
- TheoryofComputation_MISCELLANEOUS
Lyapunov function
Hessian matrix
convex optimization
Control and Optimization
Dynamical systems theory
Lyapunov analysis
MathematicsofComputing_NUMERICALANALYSIS
0211 other engineering and technologies
02 engineering and technology
Management Science and Operations Research
01 natural sciences
Article
symbols.namesake
Dynamical systems
Applied mathematics
0101 mathematics
Mathematics
021103 operations research
Weak convergence
Applied Mathematics
Newton dynamics
nonautonomous systems
010101 applied mathematics
Maxima and minima
Convex optimization
Variational inequality
symbols
Convex function
Subjects
Details
- ISSN :
- 10294945 and 02331934
- Volume :
- 68
- Database :
- OpenAIRE
- Journal :
- Optimization
- Accession number :
- edsair.doi.dedup.....33fec05ddc64e4cc0c5c68d9d54c5bcd