In this paper we propose a scalarization proximal point method to solve multiobjective unconstrained minimization problems with locally Lipschitz and quasiconvex vector functions. We prove, under natural assumptions, that the sequence generated by the method is well defined and converges globally to a Pareto-Clarke critical point. Our method may be seen as an extension, for … Read more
Filter networks are used as a powerful tool aimed at reducing the image processing time and maintaining high image quality. They are composed of sparse sub-filters whose high sparsity ensures fast image processing. The filter network design is related to solving a sparse optimization problem where a cardinality constraint bounds above the sparsity level. In … Read more
Our paper consists of two main parts. In the first one, we deal with the deterministic problem of minimizing a real valued function $f$ over the Pareto set associated with a deterministic convex bi-objective optimization problem (BOP), in the particular case where $f$ depends on the objectives of (BOP), i.e. we optimize over the Pareto … Read more
We consider the method of alternating projections for finding a point in the intersection of two possibly nonconvex closed sets. We present a local linear convergence result that makes no regularity assumptions on either set (unlike previous results), while at the same time weakening standard transversal intersection assumptions. The proof grows out of a study … Read more
This thesis aims to develop and implement both nonlinear and linear distributed optimization methods that are applicable, but not restricted to the optimal control of distributed systems. Such systems are typically large scale, thus the well-established centralized solution strategies may be computationally overly expensive or impossible and the application of alternative control algorithms becomes necessary. … Read more
We address a class of deterministic scheduling problems in which two agents compete for the usage of a single machine. The agents have their own objective functions and submit in each round an arbitrary, unprocessed task from their buffer for possible selection. In each round the smaller of the two submitted tasks is chosen and … Read more
In vector optimization with a variable ordering structure the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. In recent publications it was started to develop a comprehensive theory for these vector optimization problems. Thereby also notions of proper efficiency … Read more
This paper develops a multiattribute preference ranking rule in the context of utility robustness. A nonparametric perturbation of a given additive reference utility function is specified to solve the problem of ambiguity and inconsistency in utility assessments, while preserving the additive structure and the decision maker’s risk preference under each criterion. A concept of robust … Read more
This is the “front matter” of a new open-source book on Linear Optimization. The book and associated Matlab/AMPL/Mathematica programs are freely available from: https://sites.google.com/site/jonleewebpage/home/publications/#book Citation Jon Lee, “A First Course in Linear Optimization”, Third Edition, Reex Press, 2013-2017. Article Download View A First Course in Linear Optimization, version 3.0
Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative octant. Due to its real life applications, it is important to have practical solution approaches for computing. In this work, we consider the inexact projected gradient-like method for … Read more