Data filtering for cluster analysis by $$\ell _0$$-norm regularization

A data filtering method for cluster analysis is proposed, based on minimizing a least squares function with a weighted \(\ell _0\)-norm penalty. To overcome the discontinuity of the objective function, smooth non-convex functions are employed to approximate the \(\ell _0\)-norm. The convergence of the global minimum points of the approximating problems towards global minimum points of the original problem is stated. The proposed method also exploits a suitable technique to choose the penalty parameter. Numerical results on synthetic and real data sets are finally provided, showing how some existing clustering methods can take advantages from the proposed filtering strategy.     

Antifungal activity of essential oil from Asteriscus graveolens against postharvest phytopathogenic fungi in apples

The essential oils of the aerial parts of Asteriscus graveolens have been studied using GC and GC-MS. Twenty-eight compounds were identified in the essential oil amounting to 94.9% of the total oil. The aerial part oils showed similar chromatographic profiles and were characterized by having a high content of oxygenated sesquiterpenes with 6-oxocyclonerolidol (66.7% +/- 5.5) and 6-hydroxycyclonerolidol (8.8% +/-1.2) as the major components. The antifungal effect of the essential oil from A. graveolens leaves was evaluated in vitro against three phytopathogenic fungi of apples (Alternaria sp., Penicillium expansum, and Rhizopus stolonifer). The results suggest that this essential oil has fungicidal properties towards Alternaria sp. from direct contact assay at 0.2% (v/v) and to P. expansum from vapor assay tests at 80 microL.     

An Augmented Lagrangian Method Exploiting an Active-Set Strategy and Second-Order Information

Journal of Optimization Theory and Applications - In this paper, we consider nonlinear optimization problems with nonlinear equality constraints and bound constraints on the variables. For the...     

A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization

In this paper, we describe a two-stage method for solving optimization problems with bound constraints. It combines the active-set estimate described in Facchinei and Lucidi (J Optim Theory Appl 85(2):265–289, 1995) with a modification of the non-monotone line search framework recently proposed in De Santis et al. (Comput Optim Appl 53(2):395–423, 2012). In the first stage, the algorithm exploits a property of the active-set estimate that ensures a significant reduction in the objective function when setting to the bounds all those variables estimated active. In the second stage, a truncated-Newton strategy is used in the subspace of the variables estimated non-active. In order to properly combine the two phases, a proximity check is included in the scheme. This new tool, together with the other theoretical features of the two stages, enables us to prove global convergence. Furthermore, under additional standard assumptions, we can show that the algorithm converges at a superlinear rate. Promising experimental results demonstrate the effectiveness of the proposed method.     

Minimization over the $$\ell _1$$ -ball using an active-set non-monotone projected gradient

Computational Optimization and Applications - The $$\ell _1$$ -ball is a nicely structured feasible set that is widely used in many fields (e.g., machine learning, statistics and signal analysis)...