Related papers: Scalarization in vector optimization by functions …
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and…
Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role,…
Recent multi-task learning research argues against unitary scalarization, where training simply minimizes the sum of the task losses. Several ad-hoc multi-task optimization algorithms have instead been proposed, inspired by various…
We consider a multiobjective bilevel optimization problem with vector-valued upper- and lower-level objective functions. Such problems have attracted a lot of interest in recent years. However, so far, scalarization has appeared to be the…
We show that under a separation property, a $\mathcal{Q}$-minimal point in a normed space is the minimum of a given sublinear function. This fact provides sufficient conditions, via scalarization, for nine types of proper efficient points;…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
In this paper, we investigate the relationships between proper efficiency and the solutions of a general scalarization problem in multi-objective optimization. We provide some conditions under which the solutions of the dealt with scalar…
Langrange duality theorems for vector and set optimization problems which are based on an consequent usage of infimum and supremum (in the sense greatest lower and least upper bounds with respect to a partial ordering) have been recently…
We explore the possibility to derive basic calculus rules for some subdifferential constructions associated to set-valued maps between normed vector spaces. Then, we use these results in order to write optimality conditions for a special…
The problem of minimizing an integral functional of a vector-valued Lagrangian on a set of admissible arcs with given endpoints is considered. The problem is tackled by embedding it into a set-optimization problem such that the image space…
Training a single model on multiple input domains and/or output tasks allows for compressing information from multiple sources into a unified backbone hence improves model efficiency. It also enables potential positive knowledge transfer…
Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the lovasz extension of submodular functions provides a useful…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
This paper addresses a large class of vector optimization problems in infinite-dimensional spaces with respect to two important binary relations derived from domination structures. Motivated by theoretical challenges as well as by…
We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…
In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…
In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…
This paper provides characterizations of the weak solutions of optimization problems where a given vector function $F,$ from a decision space $X$ to an objective space $Y$, is "minimized" on the set of elements $x\in C$ (where $C\subset X$…