Related papers: Directional Pareto efficiency: concepts and optima…
We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of…
With the advent of multi-core processors, network-on-chip design has been key in addressing network performances, such as bandwidth, power consumption, and communication delays when dealing with on-chip communication between the increasing…
We consider a Ramsey model with several households with heterogeneous preferences who are able to borrow capital to each other. Since the capital constraints of one household then depends on the others' capital, one can no longer optimize…
The study of fractional variational problems in terms of a combined fractional Caputo derivative is introduced. Necessary optimality conditions of Euler-Lagrange type for the basic, isoperimetric, and Lagrange variational problems are…
The goal of multi-objective optimisation is to identify the Pareto front surface which is the set obtained by connecting the best trade-off points. Typically this surface is computed by evaluating the objectives at different points and then…
One of the most important optimality conditions to aid to solve a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality…
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…
Optimization is a critical tool for addressing a broad range of human and technical problems. However, the paradox of advanced optimization techniques is that they have maximum utility for problems in which the relationship between the…
We provide necessary and sufficient conditions for robust efficiency (in the sense of Ehrgott et al. (2014)) to multiobjective optimization problems that depend on uncertain parameters. These conditions state that a solution is robust…
This study proposes a new efficiency requirement, a minimal almost weak Pareto principle, which says that x is socially better than y whenever the only one individual never prefers y to x, and all the others prefers x to y. Then, I show…
We investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy $\epsilon$ the Pareto curve of a multiobjective optimization problem. We show that for a broad class of bi-objective problems…
This paper deals with Pareto solutions of a nonsmooth fractional interval-valued multiobjective optimization. We first introduce four types of Pareto solutions of the considered problem by considering the lower-upper interval order relation…
In this paper, we propose a new descent method, termed as multiobjective memory gradient method, for finding Pareto critical points of a multiobjective optimization problem. The main thought in this method is to select a combination of the…
Modern machine learning tasks often require considering not just one but multiple objectives. For example, besides the prediction quality, this could be the efficiency, robustness or fairness of the learned models, or any of their…
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,…
Pareto-optimality plays a central role in evaluating the efficiency of solutions to allocation problems, such as house allocation, school choice, and kidney exchange. We introduce a general linear programming problem subject to…
This paper investigates the behavior of sets and functions at infinity by introducing new concepts, namely directional normal cones at infinity for unbounded sets, along with limiting and singular subdifferentials at infinity in the…
Redistricting practitioners must balance many competing constraints and criteria when drawing district boundaries. To aid in this process, researchers have developed many methods for optimizing districting plans according to one or more…
Autonomous robots are increasingly utilized in realistic scenarios with multiple complex tasks. In these scenarios, there may be a preferred way of completing all of the given tasks, but it is often in conflict with optimal execution.…
Nervous systems, like any organismal structure, have been shaped by evolutionary processes to increase fitness. The resulting neural 'bauplan' has to account for multiple objectives simultaneously, including computational function as well…