Parametric semi-infinite optimization in certain lattices: Continuity of the feasible set

1988 ◽  
pp. 103-115 ◽  
Author(s):  
Siegfried Helbig
Keyword(s):  
Feasible Set

scholarly journals Upper-Limb Isometric Force Feasible Set: Evaluation of Joint Torque-Based Models

Biomechanics ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 102-117
Author(s):  
Nasser Rezzoug ◽  
Vincent Hernandez ◽  
Philippe Gorce
Keyword(s):  
Upper Limb ◽  
Isometric Force ◽  
Joint Torque ◽  
Force Distribution ◽  
Prediction Errors ◽  
Feasible Set ◽  
Joint Torques ◽  
Motor Abilities ◽  
Capacity Evaluation ◽  
Measured Force

A force capacity evaluation for a given posture may provide better understanding of human motor abilities for applications in sport sciences, rehabilitation and ergonomics. From data on posture and maximum isometric joint torques, the upper-limb force feasible set of the hand was predicted by four models called force ellipsoid, scaled force ellipsoid, force polytope and scaled force polytope, which were compared with a measured force polytope. The volume, shape and force prediction errors were assessed. The scaled ellipsoid underestimated the maximal mean force, and the scaled polytope overestimated it. The scaled force ellipsoid underestimated the volume of the measured force distribution, whereas that of the scaled polytope was not significantly different from the measured distribution but exhibited larger variability. All the models characterized well the elongated shape of the measured force distribution. The angles between the main axes of the modelled ellipsoids and polytopes and that of the measured polytope were compared. The values ranged from 7.3° to 14.3°. Over the entire surface of the force ellipsoid, 39.7% of the points had prediction errors less than 50 N; 33.6% had errors between 50 and 100 N; and 26.8% had errors greater than 100N. For the force polytope, the percentages were 56.2%, 28.3% and 15.4%, respectively.

scholarly journals Data-Driven Object Vehicle Estimation by Radar Accuracy Modeling with Weighted Interpolation

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2317
Author(s):  
Woo Young Choi ◽  
Jin Ho Yang ◽  
Chung Choo Chung
Keyword(s):  
Measurement Uncertainty ◽  
Relative Velocity ◽  
Tracking Error ◽  
Estimation Method ◽  
Position Error ◽  
Data Driven ◽  
Weighted Interpolation ◽  
Design Data ◽  
Feasible Set ◽  
Estimation Scheme

For accurate object vehicle estimation using radar, there are two fundamental problems: measurement uncertainties in calculating an object’s position with a virtual polygon box and latency due to commercial radar tracking algorithms. We present a data-driven object vehicle estimation scheme to solve measurement uncertainty and latency problems in radar systems. A radar accuracy model and latency coordination are proposed to reduce the tracking error. We first design data-driven radar accuracy models to improve the accuracy of estimation determined by the object vehicle’s position. The proposed model solves the measurement uncertainty problem within a feasible set for error covariance. The latency coordination is developed by analyzing the position error according to the relative velocity. The position error by latency is stored in a feasible set for relative velocity, and the solution is calculated from the given relative velocity. Removing the measurement uncertainty and latency of the radar system allows for a weighted interpolation to be applied to estimate the position of the object vehicle. Our method is tested by a scenario-based estimation experiment to validate the usefulness of the proposed data-driven object vehicle estimation scheme. We confirm that the proposed estimation method produces improved performance over the conventional radar estimation and previous methods.

Optimality and duality for vector optimization problem with non-convex feasible set

OPSEARCH ◽  
2019 ◽  
Vol 57 (1) ◽  
pp. 1-12 ◽  
Author(s):  
S. K. Suneja ◽  
Sunila Sharma ◽  
Priyanka Yadav
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Feasible Set ◽  
Optimality And Duality

scholarly journals On the Boundedness of the Feasible Set without Convexity Assumptions

1973 ◽  
Vol 14 (3) ◽  
pp. 580 ◽  
Author(s):  
Leonid Hurwicz ◽  
Stanley Reiter
Keyword(s):  
Feasible Set ◽  
Convexity Assumptions

LEXICOGRAPHIC PROBLEMS OF CONVEX OPTIMIZATION: SOLVABILITY AND OPTIMALITY CONDITIONS, CUTTING PLANE METHOD

2021 ◽  
Vol 1 ◽  
pp. 30-40
Author(s):  
Natalia V. Semenova ◽  
◽  
Maria M. Lomaga ◽  
Viktor V. Semenov ◽  
◽  
...  
Keyword(s):  
System Optimization ◽  
Cutting Plane ◽  
Recession Cone ◽  
Cutting Plane Method ◽  
Optimal Solutions ◽  
Feasible Set ◽  
Plane Method ◽  
Multicriteria Problems ◽  
Lexicographic Optimization ◽  
Feasible Solutions

The lexicographic approach for solving multicriteria problems consists in the strict ordering of criteria concerning relative importance and allows to obtain optimization of more important criterion due to any losses of all another, to the criteria of less importance. Hence, a lot of problems including the ones of com­plex system optimization, of stochastic programming under risk, of dynamic character, etc. may be presented in the form of lexicographic problems of opti­mization. We have revealed conditions of existence and optimality of solutions of multicriteria problems of lexicographic optimization with an unbounded convex set of feasible solutions on the basis of applying properties of a recession cone of a convex feasible set, the cone which puts in order lexicographically a feasible set with respect to optimization criteria and local tent built at the boundary points of the feasible set. The properties of lexicographic optimal solutions are described. Received conditions and properties may be successfully used while developing algorithms for finding optimal solutions of mentioned problems of lexicographic optimization. A method of finding lexicographic of optimal solutions of convex lexicographic problems is built and grounded on the basis of ideas of method of linearization and Kelley cutting-plane method.

scholarly journals The Smallest One-Realization of a Given Set

10.37236/1171 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Ping Zhao ◽  
Kefeng Diao ◽  
Kaishun Wang
Keyword(s):  
Open Problem ◽  
Feasible Set ◽  
Minimum Number ◽  
Chromatic Spectrum ◽  
Positive Integers ◽  
Mixed Hypergraph

For any set $S$ of positive integers, a mixed hypergraph ${\cal H}$ is a realization of $S$ if its feasible set is $S$, furthermore, ${\cal H}$ is a one-realization of $S$ if it is a realization of $S$ and each entry of its chromatic spectrum is either 0 or 1. Jiang et al. showed that the minimum number of vertices of a realization of $\{s,t\}$ with $2\leq s\leq t-2$ is $2t-s$. Král proved that there exists a one-realization of $S$ with at most $|S|+2\max{S}-\min{S}$ vertices. In this paper, we  determine the number  of vertices of the smallest one-realization of a given set. As a result, we partially solve an open problem proposed by Jiang et al. in 2002 and by Král  in 2004.

Sign in / Sign up

Export Citation Format

Share Document