Pareto-based multi-objective optimization algorithms prefer non-dominated solutions over dominated solutions and maintain as much as possible diversity in the Pareto optimal set to represent the whole Pareto-front. This paper proposes three multi-objective Artificial Bee Colony (ABC) algorithms...

In this paper, we consider a binary supervised classification problem, called spherical separation, that consists of finding, in the input space or in the feature space, a minimal volume sphere separating the set <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathcal{A}}$$</EquationSource> </InlineEquation> from the set <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${\mathcal{B}}$$</EquationSource> </InlineEquation> (i.e. a sphere enclosing all...</equationsource></inlineequation></equationsource></inlineequation>

Let E be a real reflexive strictly convex Banach space which has uniformly Gâteaux differentiable norm. Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathcal{S}=\{T(s): 0 \leq s \infty\}}$$</EquationSource> </InlineEquation> be a nonexpansive semigroup on E such that <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${Fix(\mathcal{S}) := \cap_{t\geq 0}Fix( T(t) ) \not= \emptyset}$$</EquationSource> </InlineEquation> , and f is a contraction on...</equationsource></inlineequation></equationsource></inlineequation>

In this paper, we consider a selfish bin packing problem, where each item is a selfish player and wants to minimize its cost. In our new model, if there are k items packed in the same bin, then each item pays a cost 1/k, where k ≥ 1. First we find a Nash Equilibrium (NE) in time O(n log n)...

In this paper, we discuss the performance of the DIRECT global optimization algorithm on problems with linear scaling. We show with computations that the performance of DIRECT can be affected by linear scaling of the objective function. We also provide a theoretical result which shows that...

We present an alternative proof of the Mountain Pass Theorem by means of the classical Ekeland Variational Principle for a class of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathcal{C}^1}$$</EquationSource> </InlineEquation> -functionals. In this new proof we avoid the machinery of convex analysis by a simpler characterization of the critical values of the...</equationsource></inlineequation>

Existence and location of Stackelberg equilibria is studied for two players by using appropriate variational inequalities and fixed point arguments. Both compact and non-compact strategy sets are considered in Euclidean spaces; in the non-compact case, we apply arguments from the theory of...

In this paper, we study the aggregation problem with power control under the physical interference. The maximum power is bounded. The goal is to assign power to nodes and schedule transmissions toward the sink without physical interferences such that the total number of time slots is minimized....

This article presents an analysis of the convergence order of Taylor models and McCormick-Taylor models, namely Taylor models with McCormick relaxations as the remainder bounder, for factorable functions. Building upon the analysis of McCormick relaxations by Bompadre and Mitsos (J Glob Optim...

In this paper, for a monotone operator T, we shall show strong convergence of the regularization method for Rockafellar’s proximal point algorithm under more relaxed conditions on the sequences {r <Subscript> k </Subscript>} and {t <Subscript> k </Subscript>}, <Equation ID="Equa"> <EquationSource Format="TEX">$$\lim\limits_{k\to\infty}t_k=0;\quad...</equationsource></equation></subscript></subscript>