Dear Colleagues,

During the last half century, optimization problems, consisting in minimizing a (sum and/or other combination of) convex function(s) (often subject to convex constraints), have been intensively investigated and various methods have been proposed to iteratively solve such problems. One of the most important such methods is the proximal point one introduced by Martinet and extended by Rockafellar and other authors, that it still intensively used due to the employment of the so-called splitting techniques, and thanks to direct applications in fields such as image processing and support vector machines classification problems. However, there are still many open questions and unsolved problems in this research area. For instance, the convergence of an algorithm that performs well on a class of problems is still uncertain (under standard hypotheses) or is quite slow for others.

The main concern of this Special Issue of Algorithms consists in papers dealing with iterative methods for solving convex optimization problems and applications that can be modelled as such, respectively. Special interest will be given to novel approaches to proximal point methods and significant improvements (e.g., better convergence properties or convergence under lighter hypotheses) of existing algorithms, as well as to iterative methods for solving constrained convex optimization problems. Extensions to the nonconvex case or multiobjective optimization will be taken into consideration as well, provided they are motivated by concrete applications. Investigations on connections to similar algorithms for solving monotone inclusions or dynamical systems can be considered provided the main focus of the contribution is on convex optimization problems. Among the possible application fields we note machine learning, clustering, location theory, game theory, signal processing and finance mathematics, but this list is far from being comprehensive.

Dr. Sorin-Mihai Grad
Guest Editor

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• Proximal point method
• Convex optimization problem
• Constrained optimization problem
• Splitting technique
• Image processing
• Machine learning
• Stochastic proximal algorithm
• Location theory
• Game theory