Related papers: Existence, Pareto reducibility, and connectedness …
In this article, we view the approximate version of Pareto and weak Pareto solutions of the multiobjective optimization problem through the lens of KKT type conditions. We also focus on an improved version of Geoffrion proper Pareto…
Optimizing the performance of many objectives (instantiated by tasks or clients) jointly with a few Pareto stationary solutions (models) is critical in machine learning. However, previous multi-objective optimization methods often focus on…
Lower semi-continuity (\texttt{LSC}) is a critical assumption in many foundational optimisation theory results; however, in many cases, \texttt{LSC} is stronger than necessary. This has led to the introduction of numerous weaker continuity…
In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal…
In bi-criteria optimization problems, the goal is typically to compute the set of Pareto-optimal solutions. Many algorithms for these types of problems rely on efficient merging or combining of partial solutions and filtering of dominated…
In several multiobjective decision problems Pairwise Comparison Matrices (PCM) are applied to evaluate the decision variants. The problem that arises very often is the inconsistency of a given PCM. In such a situation it is important to…
Modern machine learning models are often constructed taking into account multiple objectives, e.g., minimizing inference time while also maximizing accuracy. Multi-objective hyperparameter optimization (MHPO) algorithms return such…
We introduce two notions of effective reducibility for set-theoretical statements, based on computability with Ordinal Turing Machines (OTMs), one of which resembles Turing reducibility while the other is modelled after Weihrauch…
It is shown that the use of an external archive, purely for storage purposes, can bring substantial benefits in multi-objective optimization. A new scheme for archive management for the above purpose is described. The new scheme is combined…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
As the interest in multi- and many-objective optimization algorithms grows, the performance comparison of these algorithms becomes increasingly important. A large number of performance indicators for multi-objective optimization algorithms…
We consider optimization algorithms that are open systems, that is, with external inputs and outputs. Such algorithms arise for instance, when analyzing the effect of noise or disturbance on an algorithm, or when an algorithm is part of…
Let $f$ be a transcendental entire function and let $I(f)$ denote the set of points that escape to infinity under iteration. We give conditions which ensure that, for certain functions, $I(f)$ is connected. In particular, we show that…
How to efficiently design a communication network is a paramount task for network designing and engineering. It is, however, not a single objective optimization process as perceived by most previous researches, i.e., to maximize its…
The purpose of this note is to present my understanding of Tim Austin's proof of the multiple ergodic theorem for commuting transformations, emphasizing on the use of joinings, extensions and factors. The existence of a sated extension,…
According to the published papers and books since the turn of the century, Pareto optimization is the dominating assessment method for multi-objective nonlinear optimization problems treated by population-based optimizers like Evolutionary…
We propose a novel numerical approach to compute the Pareto front in multivariate polynomial multi-objective optimization problems. When the objective functions and (equality) constraints are multivariate polynomials, the Pareto front,…
Derivatives are an important tool for single-objective optimization. In fact, it is commonly accepted that derivative-based methods present a better performance than derivative-free optimization approaches. In this work, we will show that…
In this paper we show that two seemingly unrelated problems in economics, the hypothesis of integrability and the hypothesis of additive separability are linked by the absence of curvature of connections on webs naturally associated with…
In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for…