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作者：Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
作者单位：University of Sevilla; Copenhagen Business School
摘要：In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value, as convex objects. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective is the difference of two convex functions (DC). Suitable DC decompositions allow us to use the Difference of Convex Algorithm (DCA) in a very efficient way. Our algorithmic approach...
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作者：Maehara, Takanori; Marumo, Naoki; Murota, Kazuo
作者单位：Shizuoka University; RIKEN; University of Tokyo; Tokyo Metropolitan University
摘要：Discrete DC programming with convex extensible functions is studied. A natural approach for this problem is a continuous relaxation that extends the problem to a continuous domain and applies the algorithm in continuous DC programming. By employing a special form of continuous relaxation, which is named lin-vex extension, the produced optimal solution of the extended continuous relaxation coincides with the solution of the original discrete problem. The proposed method is demonstrated for the ...
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作者：Teboulle, Marc
作者单位：Tel Aviv University
摘要：We discuss the foundational role of the proximal framework in the development and analysis of some iconic first order optimization algorithms, with a focus on non-Euclidean proximal distances of Bregman type, which are central to the analysis of many other fundamental first order minimization relatives. We stress simplification and unification by highlighting self-contained elementary proof-patterns to obtain convergence rate and global convergence both in the convex and the nonconvex settings...
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作者：Arpon, Sebastian; Homem-de-Mello, Tito; Pagnoncelli, Bernardo
作者单位：Universidad Adolfo Ibanez
摘要：In this paper we discuss scenario reduction methods for risk-averse stochastic optimization problems. Scenario reduction techniques have received some attention in the literature and are used by practitioners, as such methods allow for an approximation of the random variables in the problem with a moderate number of scenarios, which in turn make the optimization problem easier to solve. The majority of works for scenario reduction are designed for classical risk-neutral stochastic optimization...
