  


Concave programming for minimizing the zeronorm over polyhedral sets
Francesco Rinaldi(frinaldiiasi.cnr.it) Abstract: Given a non empty polyhedral set, we consider the problem of finding a vector belonging to it and having the minimum number of nonzero components, i.e., a feasible vector with minimum zeronorm. This nonsmooth combinatorial optimization problem is NPHard and arises in various fields such as machine learning, pattern recognition, signal processing. We propose two smooth approximations of the zeronorm function, where the approximating functions are separable and concave. We formally prove the equivalence between the approximating problems and the original nonsmooth problem. To this aim, we preliminarly state in a general setting theoretical conditions sufficient to guarantee the equivalence between pairs of problems. We also define an effective version of the FrankWolfe algorithm for the minimization of concave separable functions over polyhedral sets, and we prove the global convergence of the method. Finally, we report the numerical results on test problems showing both the usefulness of the new concave formulations and the efficiency in terms of computational time of the implemented minimization algorithm. Keywords: Zeronorm, concave optimization, FrankWolfe algorithm Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization ) Category 2: Applications  Science and Engineering (DataMining ) Citation: TR DSI 2008/02 Download: [PDF] Entry Submitted: 03/25/2008 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  