Minimizing nonsmooth DC functions via successive DC piecewise-affine approximations

Gaudioso, Manlio; Giallombardo, Giovanni; Miglionico, Giovanna; Bagirov, Adil M.

doi:10.1007/s10898-017-0568-z

Cited by 56 publications

(29 citation statements)

References 22 publications

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“…Denoting the set of inf-stationary points by S in f , the set of Clarke stationary points by S cl , and the set of critical points of the function f by S cr , the following inclusions hold S in f ⊆ S cl ⊆ S cr as shown in (Proposition 3, [30]).…”

Section: Solving Dc-mil Using a Nonsmooth DC Algorithmmentioning

confidence: 99%

“…In the last years, nonsmooth-tailored DC programming has experienced a lot of attention as it has a lot of practical applications (see [28,42]). In fact, several nonsmooth DC algorithms have been developed ( [30,[43][44][45][46][47]).…”

Section: Solving Dc-mil Using a Nonsmooth DC Algorithmmentioning

confidence: 99%

“…Recently, nonlinear instance-space MIL classifiers have also been proposed in the literature, such as in [27] and in [28], where a spherical separation approach is adopted: in particular, in the former a variable neighborhood search method [29] is used, while in the latter a DC (difference of convex) model is solved using an appropriate DC algorithm [30]. In passing, we stress that many DC models have been introduced in machine learning, in the supervised [31][32][33][34][35], semisupervised [36,37] and unsupervised cases [38][39][40].…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we propose a DC optimization model providing a linear classifier for binary MIL problems. The solution method we adopt is the proximal bundle method introduced in [30] for the minimization of nonsmooth DC functions. The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

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SVM-Based Multiple Instance Classification via DC Optimization

et al. 2019

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A multiple instance learning problem consists of categorizing objects, each represented as a set (bag) of points. Unlike the supervised classification paradigm, where each point of the training set is labeled, the labels are only associated with bags, while the labels of the points inside the bags are unknown. We focus on the binary classification case, where the objective is to discriminate between positive and negative bags using a separating surface. Adopting a support vector machine setting at the training level, the problem of minimizing the classification-error function can be formulated as a nonconvex nonsmooth unconstrained program. We propose a difference-of-convex (DC) decomposition of the nonconvex function, which we face using an appropriate nonsmooth DC algorithm. Some of the numerical results on benchmark data sets are reported.

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Section: Solving Dc-mil Using a Nonsmooth DC Algorithmmentioning

confidence: 99%

Section: Solving Dc-mil Using a Nonsmooth DC Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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SVM-Based Multiple Instance Classification via DC Optimization

et al. 2019

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“…• A proximal bundle method for the numerical minimization of a non-smooth DC function is introduced in [3]. The authors build two piecewise-affine approximations of the component functions, grouping the corresponding information in two separate bundles.…”

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confidence: 99%