An optimal control problem for a semilinear heat equation with distributed is discussed, where two-sided pointwise box constraints on the and mixed control-state are given. The objective functional sum of standard quadratic tracking type part multiple L 1 -norm that accounts sparsity. Under certain structural condition almost active sets solution, existence integrable Lagrange multipliers prove...

An effective approach to structure learning and parameter estimation for Gaussian graphical models is to impose a sparsity prior, such as a Laplace prior, on the entries of the precision matrix. Such an approach involves a hyperparameter that must be tuned to control the amount of sparsity. In this paper, we introduce a parameter-free method for estimating a precision matrix with sparsity that ...

Based on the recent mathematical findings on solving the linear inverse problems with sparsity constraints by Daubechiesx et al., here we adapt a simultaneous algebraic reconstruction technique (SART) for image reconstruction from a limited number of projections subject to a sparsity constraint in terms of an invertible compression transform. The algorithm is implemented with an exemplary Haar ...

Sparsity-inducing norm has been a powerful tool for learning robust models with limited data in high dimensional space. By imposing such norms as constraints or regularizers in an optimization setting, one could bias the model towards learning sparse solutions, which in many case have been proven to be more statistically efficient [Don06]. Typical sparsityinducing norms include `1 norm [Tib96] ...

OBJECTIVE Electroencephalography (EEG) and magnetoencephalography (MEG) non-invasively record scalp electromagnetic fields generated by cerebral currents, revealing millisecond-level brain dynamics useful for neuroscience and clinical applications. Estimating the currents that generate these fields, i.e., source localization, is an ill-conditioned inverse problem. Solutions to this problem have...

We develop a highly scalable optimization method called “hierarchical group-thresholding” for solving a multi-task regression model with complex structured sparsity constraints on both input and output spaces. Despite the recent emergence of several efficient optimization algorithms for tackling complex sparsity-inducing regularizers, true scalability in practical high-dimensional problems wher...