Feasible region

Résumé

In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down. For example, consider the problem of minimizing the function x^2+y^4 with respect to the variables x and y, subject to 1 \le x \le 10 and 5 \le y \le 12. , Here the feasible set is the set of pairs (x, y) in which the value of x is at least 1 and at most 10 and the value of y is at least 5 and at most 12. The feasible set of the problem is separate from the objective function, which states the criterion to be optimized and which in the above example is x^2+y^4. In many problems

Source officielle

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Publications associées

Chargement

Personnes associées

Chargement

Unités associées

Chargement

Concepts associés

Chargement

Cours associés

Chargement

Séances de cours associées

Chargement

Virtual Landmark-Based Control of Docking Support for Assistive Mobility Devices

Diego Felipe Paez Granados, Chen Yang

This work proposes an autonomous docking control for nonholonomic constrained mobile robots and applies it to an intelligent mobility device or wheelchair for assisting the user in approaching resting furniture such as a chair or a bed. We defined a virtual landmark inferred from the target docking destination. Then we solve the problem of keeping the targeted volume inside the field of view (FOV) of a tracking camera and docking to the virtual landmark through a novel definition that enables to control for the desired end-pose. We proposed a nonlinear feedback controller to perform the docking with the depth camera’s FOV as a constraint. Then a numerical method is proposed to find the feasible space of initial states where convergence could be guaranteed. Finally, the entire system was embedded for real-time operation on a standing wheelchair with the virtual landmark estimation by 3D object tracking with an RGB-D camera and we validated the effectiveness in simulation and experimental evaluations. The results show the guaranteed convergence for the feasible space depending on the virtual landmark location. In the implementation, the robot converges to the virtual landmark while respecting the FOV constraints.

2021

Chargement

In the present paper, a model of a solar tower power plant (STPP) is presented. This is the result of a Master semester project led at the Laboratory for Industrial Energetic Systems (LENI) at the Swiss Federal Institute in Lausanne (EPFL). The modelized plant uses molten salt as heat transfer fluid (HTF), within a circuit including a direct storage system. The hot salt is used to provide power to a conventional Rankine cycle based on steam. For this first step a Rankine cycle without any improvement is modelled, in order to provide a simple running model being subject to improvements later. The model is realized using the program Vali, allowing to submit it to a multicriteria optimization algorithm, aiming the best feasible solution seen from a thermo-economic point of view. This report is exposing the work done on the model. The modelling of certain details is carefully described, then the operating parameters used for the model validation are presented. The results are then exposed in details, including several different strategies for the usage of the stored mass. A discussion of the presented results is then led, the results being compared to those of an unknown solar power plant (Solar Two). Finally, the major points that are subject to improvements are listed and the further work to be done is detailed.

2009

Chargement

Stochastic programming and distributionally robust optimization seek deterministic decisions that optimize a risk measure, possibly in view of the most adverse distribution in an ambiguity set. We investigate under which circumstances such deterministic decisions are strictly outperformed by random decisions which depend on a randomization device producing uniformly distributed samples that are independent of all uncertain factors affecting the decision problem. We find that in the absence of distributional ambiguity, deterministic decisions are optimal if both the risk measure and the feasible region are convex, or alternatively if the risk measure is mixture-quasiconcave. We show that several classes of risk measures, such as mean (semi-)deviation and mean (semi-)moment measures, fail to be mixture-quasiconcave and can therefore give rise to problems in which the decision maker benefits from randomization. Under distributional ambiguity, on the other hand, we show that for any ambiguity averse risk measure there always exists a decision problem (with a nonconvex—e.g., mixed-integer—feasible region) in which a randomized decision strictly dominates all deterministic decisions.

2019

Chargement