Related papers: Proper efficiency and cone efficiency

Pairwise comparison matrices are frequently applied in multi-criteria decision making. A weight vector is called efficient if no other weight vector is at least as good in approximating the elements of the pairwise comparison matrix, and…

This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…

In this paper we consider well-posedness properties of vector optimization problems with objective function $f: X \to Y$ where $X$ and $Y$ are Banach spaces and $Y$ is partially ordered by a closed convex pointed cone with nonempty…

In this paper, we propose a Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The objective function of the problem under consideration is given by…

There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of…

Efficient global optimization is the problem of minimizing an unknown function f, using as few evaluations f(x) as possible. It can be considered as a continuum-armed bandit problem, with noiseless data and simple regret. Expected…

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

We develop \emph{geometric optimisation} on the manifold of Hermitian positive definite (HPD) matrices. In particular, we consider optimising two types of cost functions: (i) geodesically convex (g-convex); and (ii) log-nonexpansive (LN).…

In a Hilbertian framework, for the minimization of a general convex differentiable function $f$, we introduce new inertial dynamics and algorithms that generate trajectories and iterates that converge fastly towards the minimizer of $f$…

We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and Nemirovskii in the early 1990s to a broader class of convex functions, which we call generalized…

In solving a multi-objective optimization problem by scalarization techniques, solutions to a scalarized problem are, in general, weakly efficient rather than efficient to the original problem. Thus, it is crucial to understand what problem…

Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…

Optimization models generally aim for efficiency by maximizing total benefit or minimizing cost. Yet a trade-off between fairness and efficiency is an important element of many practical decisions. We propose a principled and practical…

In this paper, we develop a novel unified methodology for performance and robustness analysis of linear dynamical networks. We introduce the notion of systemic measures for the class of first--order linear consensus networks. We classify…

We consider the minimization of a continuous function over the intersection of a regular cone with an affine set via a new class of adaptive first- and second-order optimization methods, building on the Hessian-barrier techniques introduced…

The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved non convex…

This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower…

This work addresses arbitrary convex vector optimization problems, which constitute a general framework for multi-criteria decision-making in diverse real-world applications. Due to their complexity, such problems are typically tackled…

Since the breakthrough performance of AlexNet in 2012, convolutional neural networks (convnets) have grown into extremely powerful vision models. Deep learning researchers have used convnets to perform vision tasks with accuracy that was…

A convex cone is homogeneous if its automorphism group acts transitively on the interior of the cone, i.e., for every pair of points in the interior of the cone, there exists a cone automorphism that maps one point to the other. Cones that…