Related papers: BI - level programming
Many engineering optimization problems can be considered as linear programming problems where all or some of the parameters involved are linguistic in nature. These can only be quantified using fuzzy sets. The aim of this paper is to solve…
Bilevel optimization is a powerful tool for modeling hierarchical decision making processes. However, the resulting problems are challenging to solve - both in theory and practice. Fortunately, there have been significant algorithmic…
Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics,…
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…
This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…
The multiresponse surface problem is modelled as one of multiobjective stochastic optimisation, and diverse solutions are proposed. Several crucial differences are highlighted between this approach and others that have been proposed.…
We consider a bilevel optimization problem in which the ground set is partitioned between two decision makers, a leader and a follower, whose optimization problems are interleaved. We study the Bilevel Independent Set problem, and its…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
We consider parametric linear programming problems with multiple objective functions depending linearly on some parameter. Both parametric (single-objective) linear programming and (non-parametric) multi-objective linear programming are…
A fuzzy clustering algorithm for multidimensional data is proposed in this article. The data is described by vectors whose components are linguistic variables defined in an ordinal scale. The obtained results confirm the efficiency of the…
We present a logical framework to represent and reason about fuzzy optimization problems based on fuzzy answer set optimization programming. This is accomplished by allowing fuzzy optimization aggregates, e.g., minimum and maximum in the…
Fuzzy systems show strong potential in explainable AI due to their rule-based architecture and linguistic variables. Existing approaches navigate the accuracy-explainability trade-off either through evolutionary multi-objective optimization…
Diffusion models, which iteratively denoise data samples to synthesize high-quality outputs, have achieved empirical success across domains. However, optimizing these models for downstream tasks often involves nested bilevel structures,…
In this paper, we study a fixed-confidence, fixed-tolerance formulation of a class of stochastic bi-level optimization problems, where the upper-level problem selects from a finite set of systems based on a performance metric, and the…
Multiobjective stochastic programming is a field well located to tackle problems arising in emergencies, given that uncertainty and multiple objectives are usually present in such problems. A new concept of solution is proposed in this…
Bilevel programming is one of the very active areas of research with many real-life applications in economics and engineering. Bilevel problems are hierarchical problems consisting of lower-level and upper-level problems, respectively. The…
Bilevel optimization deals with nested problems in which a leader takes the first decision to minimize their objective function while accounting for a follower's best-response reaction. Constrained bilevel problems with integer variables…
Linear superiorization (abbreviated: LinSup) considers linear programming (LP) problems wherein the constraints as well as the objective function are linear. It allows to steer the iterates of a feasibility-seeking iterative process toward…
We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical…
Here, necessary optimal condition for Optimistic Bilevel programming problem is obtained in Asplund spaces. Also we have got necessary optimal conditions in finite dimensional spaces, by assuming differentiability on the given functions.