On numerical solving the spherical separability problem

Gaudioso, Manlio; Gruzdeva, Tatiana V.; Strekalovsky, Alexander S.

doi:10.1007/s10898-015-0319-y

Cited by 9 publications

(1 citation statement)

References 29 publications

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“…Moreover, due to the fact that a DC decomposition is not unique, the found DC decompostion may not be the most suitable one. However, there exist many practical applications where the objectives are in the explicit DC form, like in clustering [2], spherical separability problems [11], productiontransportation planning [15], wireless sensor network planning [1], and data visualization [5]. It is worth noticing that these applications usually either model the problem directly as a single-objective problem or scalarize a biobjective problem, even if they have multiobjective nature.…”

Section: Introduction To Multiobjective DC Optimizationmentioning

confidence: 99%

Multiobjective Double Bundle Method for DC Optimization

Montonen

Joki

2020

Numerical Nonsmooth Optimization

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We discuss about the multiobjective double bundle method for nonsmooth multiobjective optimization where objective and constraint functions are presented as a difference of two convex (DC) functions. By utilizing a special technique called the improvement function, we are able to handle several objectives and constraints simultaneously. The method improves every objective at each iteration and the improvement function preserves DC property of the objectives and constraints. Once the improvement function is formed, we can approximate it by using a special cutting plane model capturing the convex and concave behaviour of a DC function. We solve the problem with a modified version of the single-objective double bundle method using the cutting plane model as a objective. The multiobjective double bundle method is proved to be finitely convergent to a weakly Pareto stationary solution under mild assumptions. Moreover, the applicability of the method is considered.

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