First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking...First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes applied to infinite-dimensional elliptic optimal control problems and to validate the theoretical estimates.展开更多
In this paper,a new Hilbert space is defined which is embedded into W01,q(Ω)for 1≤q<2.By using sign-changing critical point theory,we prove the existence of infinitely many sign-changing solutions in this new spa...In this paper,a new Hilbert space is defined which is embedded into W01,q(Ω)for 1≤q<2.By using sign-changing critical point theory,we prove the existence of infinitely many sign-changing solutions in this new space for nonlinear elliptic partial differential equations with Hardy potential and critical parameter in R2.展开更多
文摘First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes applied to infinite-dimensional elliptic optimal control problems and to validate the theoretical estimates.
基金Supported by Science and Technology Foundation of Guizhou Province of China under Grant Qiankehe-J-LKM[2012]19
文摘In this paper,a new Hilbert space is defined which is embedded into W01,q(Ω)for 1≤q<2.By using sign-changing critical point theory,we prove the existence of infinitely many sign-changing solutions in this new space for nonlinear elliptic partial differential equations with Hardy potential and critical parameter in R2.
