Solution of a tropical optimization problem with linear constraints

2015 ◽  
Vol 48 (4) ◽  
pp. 224-232 ◽  
Author(s):  
N. K. Krivulin ◽  
V. N. Sorokin
Keyword(s):  
Optimization Problem ◽  
Linear Constraints ◽  
Tropical Optimization

Practical Tools for Reasoning About Linear Constraints

1991 ◽  
Vol 15 (3-4) ◽  
pp. 357-379
Author(s):  
Tien Huynh ◽  
Leo Joskowicz ◽  
Catherine Lassez ◽  
Jean-Louis Lassez
Keyword(s):  
Logic Programming ◽  
Intelligent Systems ◽  
Optimization Problem ◽  
Spatial Reasoning ◽  
Quantifier Elimination ◽  
Canonical Representation ◽  
Linear Constraints ◽  
Practical Applications ◽  
Variable Elimination ◽  
Fourier Algorithm

We address the problem of building intelligent systems to reason about linear arithmetic constraints. We develop, along the lines of Logic Programming, a unifying framework based on the concept of Parametric Queries and a quasi-dual generalization of the classical Linear Programming optimization problem. Variable (quantifier) elimination is the key underlying operation which provides an oracle to answer all queries and plays a role similar to Resolution in Logic Programming. We discuss three methods for variable elimination, compare their feasibility, and establish their applicability. We then address practical issues of solvability and canonical representation, as well as dynamical updates and feedback. In particular, we show how the quasi-dual formulation can be used to achieve the discriminating characteristics of the classical Fourier algorithm regarding solvability, detection of implicit equalities and, in case of unsolvability, the detection of minimal unsolvable subsets. We illustrate the relevance of our approach with examples from the domain of spatial reasoning and demonstrate its viability with empirical results from two practical applications: computation of canonical forms and convex hull construction.

A Dynamics-Based Optimal Trajectory Generation for Controlling an Automated Excavator

2010 ◽  
Vol 224 (10) ◽  
pp. 2109-2119 ◽  
Author(s):  
S Yoo ◽  
C-G Park ◽  
S-H You ◽  
B Lim
Keyword(s):  
Optimal Trajectory ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Linear Constraints ◽  
Control Points ◽  
Weighting Functions ◽  
B Splines ◽  
Finite Dimensional ◽  
Motion Optimization ◽  
Save Energy

This article presents a new methodology to generate optimal trajectories in controlling an automated excavator. By parameterizing all the actuator displacements with B-splines of the same order and with the same number of control points, the coupled actuator limits, associated with the maximum pump flowrate, are described as the finite-dimensional set of linear constraints to the motion optimization problem. Several weighting functions are introduced on the generalized actuator torque so that the solution to each optimization problems contains the physical meaning. Numerical results showing that the generated motions of the excavator are fairly smooth and effectively save energy, which can prevent mechanical wearing and possibly save fuel consumption, are presented. A typical operator's manoeuvre from experiments is referred to bring out the standing features of the optimized motion.

Research on Precise Constraint Reconstruction of Section Data

2013 ◽  
Vol 712-715 ◽  
pp. 1122-1125
Author(s):  
Xu Zhang ◽  
Hai Bo Zhang ◽  
Xue Chang Zhang
Keyword(s):  
Objective Function ◽  
Optimization Problem ◽  
Linear Constraints ◽  
Reconstruction Method ◽  
Linear Boundary ◽  
Reconstruction Accuracy ◽  
B Spline ◽  
Boundary Constraints ◽  
Real Application ◽  
Section Data

Since the features are not prominent and the algorithm is complex during whole reconstruction of section data, a step-by-step optimization reconstruction method is proposed. The order of reconstruction is optimized: line features are reconstructed firstly; Then arc features are reconstructed (constraints are satisfied between the arc and known lines); finally freeform features are reconstructed (constraints are satisfied between the B-spline and known lines/arcs). In this way, the reconstruction accuracy of the line/arc features is ensured in the first. Since freeform features have more freedom, it is convenient to be adjusted to meet the more constraints. Linear boundary constraints are constructed and the algorithm becomes optimization problem of the quadratic objective function under the linear constraints. The examples show that the reconstruction accuracy is improved greatly under satisfying constraints; the expected goal is achieved in real application.

scholarly journals Solving Optimization Problem under Stochastic Max-Min Separable Linear Constraints

2021 ◽  
Vol 10 (4) ◽  
pp. 80-89
Author(s):  
Hanaa Khater ◽  
Ahmed El-Sawy ◽  
Assem Tharwat ◽  
Ihab El-Khodary
Keyword(s):  
Optimization Problem ◽  
Linear Constraints

scholarly journals Maximizing Compound Poisson Stop-Loss Premiums Numerically with Given Mean and Variance

1992 ◽  
Vol 22 (2) ◽  
pp. 225-233 ◽  
Author(s):  
R. Kaas ◽  
M. Vanneste ◽  
M.J. Goovaerts
Keyword(s):  
Linear Function ◽  
Optimization Problem ◽  
Linear Constraints ◽  
Finite Support ◽  
Compound Poisson ◽  
Non Linear ◽  
Mean And Variance ◽  
Stop Loss

AbstractThis paper describes a technique to find the maximal stop-loss premiums in a given retention for a compound Poisson risk with known parameter, and known mean and variance of the claims. Restricting to an arithmetic and finite support of the claims, one gets an optimization problem of a non-linear function with a computable gradient, under linear constraints.Numeraical results are given contrasting the method with the method of a previous paper, where only diatomic distributions were considered.

scholarly journals Sobre la síntesis óptima de mecanismos

2019 ◽  
pp. 16-22
Author(s):  
Ixshel Jhoselyn Foster-Vázquez ◽  
Rogelio De Jesús Portillo-Vélez ◽  
Eduardo Vazquez-Santacruz
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Great Influence ◽  
General Rule ◽  
Linear Constraints ◽  
Synthesis Problem ◽  
Mechanism Synthesis ◽  
Problem Statement ◽  
Engineering Design Process ◽  
The Impact

In the engineering design process, it is of particular relevance the problem statement that has to be solved to guarantee an optimal design. There is no general rule for this, and in the particular case of the synthesis of flat mechanisms, the solution strongly depends on the problem statement for the design or mechanism synthesis. The object this paper is presenting one proposal at synthesis problem of a four-bar flat mechanism for cartesian trajectory tracking. The mechanism synthesis problem is stated as a nonlinear optimization problem with non linear constraints. Four different approaches are considered in order to demonstrate the impact of the considered statement of the optimization problem for its solution. The solution of the four optimization problems is obtained by means of numerical calculations using genetic algorithms. The numerical results of the four optimization problem statemens are compared under fair circumstances and they depict the great influence of the initial problem statement for its solution.

scholarly journals A Robust Transmission Scheduling Approach for Internet of Things (IoT) Sensing Service with Energy Harvesting

Sensors ◽  
2019 ◽  
Vol 19 (14) ◽  
pp. 3090
Author(s):  
Jie Hao ◽  
Jing Chen ◽  
Ran Wang ◽  
Yi Zhuang ◽  
Baoxian Zhang
Keyword(s):  
Internet Of Things ◽  
Optimization Problem ◽  
Linear Constraints ◽  
Optimization Approach ◽  
Transmission Scheduling ◽  
Scheduling Optimization ◽  
Energy Constraint ◽  
Sophisticated Model ◽  
Robust Transmission ◽  
Good Trade

Maximizing the utility under energy constraint is critical in an Internet of Things (IoT) sensing service, in which each sensor harvests energy from THE ambient environment and uses it for sensing and transmitting the measurements to an application server. Such a sensor is required to maximize its utility under THE harvested energy constraint, i.e., perform sensing and transmission at the highest rate allowed by the harvested energy constraint. Most existing works assumed a sophisticated model for harvested energy, but neglected the fact that the harvested energy is random in reality. Considering the randomness of the harvested energy, we focus on the transmission scheduling issue and present a robust transmission scheduling optimization approach that is able to provide robustness against randomness. We firstly formulate the transmission scheduling optimization problem subject to energy constraints with random harvested energy. We then introduce a flexible model to profile the harvested energy so that the constraints with random harvested energy are transformed into linear constraints. Finally, the transmission scheduling optimization problem can be solved traditionally. The experimental results demonstrate that the proposed approach is capable of providing a good trade-off between service flexibility and robustness.

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