We introduce a bundle method for the unconstrained minimization of nonsmooth difference-of-convex (DC) functions, and it is based on the calculation of a special type of descent direction called descent–ascent direction. The algorithm only requires evaluations of the minuend component function at each iterate, and it can be considered as a parsimonious bundle method as accumulation of information takes place only in case the descent–ascent direction does not provide a sufficient decrease. No line search is performed, and proximity control is pursued independent of whether the decrease in the objective function is achieved. Termination of the algorithm at a point satisfying a weak criticality condition is proved, and numerical results on a set of benchmark DC problems are reported. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms – Continuous. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0142 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0142 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Among skin cancers, melanoma is the most aggressive and most lethal form. Despite these terrible premises, an excision treatment carried out thanks to an early diagnosis is almost always decisive, guaranteeing the patient's survival. The early detection of melanoma is hampered by the extreme similarity of melanoma with other skin lesions such as dysplastic nevi. The current research is aimed at defining software solutions that support the computerized diagnosis of lesions for the detection of melanoma. To date, the proposals, both in terms of algorithms and frameworks, have focused on the dichotomous distinction of melanoma from benign lesions. However, the current debate on Dysplastic Nevi Syndrome (DNS), makes issues relating to the nature of the lesions, central to subjects who present a large number of moles throughout the body. In fact, individuals with DNS have a greater chance of being attacked by melanoma. The classification task relating to the distinction of dysplastic nevi from common ones is totally unexplored. In this document, we consider the difficult task of applying multiple-instance learning (MIL) approaches to discriminate melanoma from dysplastic nevi and outline an even more complex challenge related to the classification of dysplastic nevi from common ones. In particular, we introduce the application of a MIL approach that uses spherical separation surfaces. Since the results seem promising, we conclude that a MIL technique could be the basis of more sophisticated tools useful for detecting skin lesions.