In this paper, optimality conditions for the group sparse constrained optimization (GSCO) problems are studied. Firstly, equivalent characterizations of Bouligand tangent cone, Clarke cone and their corresponding normal cones set derived. Secondly, by using cones, four types stationary points GSCO given: TB-stationary point, NB-stationary TC-stationary point NC-stationary which used to characte...

The pathwise coordinate optimization is one of the most important computational frameworks for high dimensional convex and nonconvex sparse learning problems. It differs from the classical coordinate optimization algorithms in three salient features: warm start initialization, active set updating, and strong rule for coordinate preselection. Such a complex algorithmic structure grants superior ...

Sparse and convolutional constraints form a natural prior for many optimization problems that arise from physical processes. Detecting motifs in speech and musical passages, super-resolving images, compressing videos, and reconstructing harmonic motions can all leverage redundancies introduced by convolution. Solving problems involving sparse and convolutional constraints remains a difficult co...

We propose a technique of multisensor signal reconstruction based on the assumption, that source signals are spatially sparse, as well as have sparse representation in a chosen dictionary in time domain. This leads to a large scale convex optimization problem, which involves combined l1-l2 norm minimization. The optimization is carried by the truncated Newton method, using preconditioned conjug...

3 Sparse Representation and DOA estimation 7 3.1 Sparse Representation and Compressed Sensing . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1.2 Convex Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.3 `q Optimization . . . . . . . . . . . . . . . . . . . ....

In this paper, we propose a primal interior-point method for large sparse minimax optimization. After a short introduction, the complete algorithm is introduced and important implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus the large sparse nonconvex minimax optimization problems can be solved successfully. The results o...

We propose a technique of multisensor signal reconstruction based on the assumption, that source signals are spatially sparse, as well as have sparse representation in a chosen dictionary in time domain. This leads to a large scale convex optimization problem, which involves combined l1-l2 norm minimization. The optimization is carried by the truncated Newton method, using preconditioned conjug...