A Time-Stepping Scheme for Quasistatic Multibody Systems

2005 ◽  
Author(s):  
J. C. Trinkle ◽  
Stephen Berard ◽  
J. S. Pang
Keyword(s):  
Three Dimensional ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Contact Forces ◽  
Global Optimal Solution ◽  
Convex Optimization Problem ◽  
Time Stepping ◽  
Global Optimal ◽  
Necessary And Sufficient ◽  
First Time

Two new instantaneous-time models for predicting the motion and contact forces of three-dimensional, quasistatic multi-rigid-body systems are developed; one linear and one nonlinear. The nonlinear characteristic is the result of retaining the usual quadratic friction cone in the model. Discrete-time versions of these models provide the first time-stepping methods for such systems. As a first step to understanding their usefulness in simulation and manipulation planning, a theorem defining the equivalence of solutions of a time-stepping method for the nonlinear model and a global optimal solution of a related convex optimization problem is given. In addition, a Proposition giving necessary and sufficient conditions for solution uniqueness of the nonlinear time-stepping method is given. Finally, a simple example is discussed to help develop intuition about quasistatic systems and to solidify the reader’s understanding of the theorem and proposition.

scholarly journals Quadratic problems with two quadratic constraints: convex quadratic relaxation and strong Lagrangian duality

2020 ◽  
Author(s):  
Abdelouahed Hamdi ◽  
Akram Taati ◽  
Temadher A Almaadeed
Keyword(s):  
Sufficient Conditions ◽  
Optimal Solution ◽  
Lagrangian Duality ◽  
Global Optimality ◽  
Global Optimal Solution ◽  
Quadratic Constraints ◽  
Quadratic Minimization ◽  
Global Optimal ◽  
Necessary And Sufficient ◽  
Convex Quadratic Relaxation

In this paper,  we study  a nonconvex quadratic minimization problem with two quadratic constraints, one of which being convex.  We introduce two convex quadratic relaxations (CQRs) and discuss cases, where the problem is equivalent to exactly one of the CQRs. Particularly, we show that the global optimal  solution can be recovered from an optimal solution of the CQRs. Through this equivalence, we introduce new conditions under which the problem enjoys strong Lagrangian duality, generalizing  the recent  condition  in the literature.  Finally, under the new conditions,  we present  necessary and sufficient conditions for global optimality of the problem.

scholarly journals A New Methodology to Establish Upper Bounds on Open-Cell Foams Homogenized Properties

10.14311/652 ◽  
2004 ◽  
Vol 44 (5-6) ◽  
Author(s):  
Z. Dimitrovová
Keyword(s):  
Three Dimensional ◽  
Sufficient Conditions ◽  
Upper Bounds ◽  
Geometrical Parameters ◽  
Open Cell ◽  
Linear Elastic ◽  
Internal Forces ◽  
Open Cell Foams ◽  
Necessary And Sufficient ◽  
First Time

The methodology for determining the upper bounds on the homogenized linear elastic properties of cellular solids, described for the two-dimensional case in Dimitrovová and Faria (1999), is extended to three-dimensional open-cell foams. Besides the upper bounds, the methodology provides necessary and sufficient conditions on optimal media. These conditions are written in terms of generalized internal forces and geometrical parameters. In some cases dependence on internal forces can be replaced by geometrical expressions. In such cases, the optimality of some medium under consideration can be verified directly from the microstructure, without any additional calculation. Some of the bounds derived in this paper are published for the first time, along with a proof of their optimality. 

AO-BBO: A Novel Optimization Algorithm and Its Application in Plant Drug Extraction

2019 ◽  
Vol 19 (2) ◽  
pp. 139-145 ◽  
Author(s):  
Bote Lv ◽  
Juan Chen ◽  
Boyan Liu ◽  
Cuiying Dong
Keyword(s):  
Optimization Algorithm ◽  
Learning Strategy ◽  
Optimal Solution ◽  
Population Diversity ◽  
Global Optimal Solution ◽  
Plant Medicine ◽  
Suitability Index ◽  
Sensing Model ◽  
Local Optimal Solution ◽  
Global Optimal

<P>Introduction: It is well-known that the biogeography-based optimization (BBO) algorithm lacks searching power in some circumstances. </P><P> Material & Methods: In order to address this issue, an adaptive opposition-based biogeography-based optimization algorithm (AO-BBO) is proposed. Based on the BBO algorithm and opposite learning strategy, this algorithm chooses different opposite learning probabilities for each individual according to the habitat suitability index (HSI), so as to avoid elite individuals from returning to local optimal solution. Meanwhile, the proposed method is tested in 9 benchmark functions respectively. </P><P> Result: The results show that the improved AO-BBO algorithm can improve the population diversity better and enhance the search ability of the global optimal solution. The global exploration capability, convergence rate and convergence accuracy have been significantly improved. Eventually, the algorithm is applied to the parameter optimization of soft-sensing model in plant medicine extraction rate. Conclusion: The simulation results show that the model obtained by this method has higher prediction accuracy and generalization ability.</P>

scholarly journals Best Proximity Point Results in Complex Valued Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Binayak S. Choudhury ◽  
Nikhilesh Metiya ◽  
Pranati Maity
Keyword(s):  
Minimum Distance ◽  
Metric Spaces ◽  
Optimal Solution ◽  
Global Optimal Solution ◽  
Complex Valued Metric Space ◽  
Fixed Point Equation ◽  
Point Equation ◽  
Global Optimal ◽  
Metric Function ◽  
Complex Valued

We introduce the concept of proximity points for nonself-mappings between two subsets of a complex valued metric space which is a recently introduced extension of metric spaces obtained by allowing the metric function to assume values from the field of complex numbers. We apply this concept to obtain the minimum distance between two subsets of the complex valued metric spaces. We treat the problem as that of finding the global optimal solution of a fixed point equation although the exact solution does not in general exist. We also define and use the concept of P-property in such spaces. Our results are illustrated with examples.

scholarly journals Prototype Filter Design Based on Channel Estimation for FBMC/OQAM Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yongjin Liu ◽  
Xihong Chen ◽  
Yu Zhao
Keyword(s):  
Genetic Algorithm ◽  
Channel Estimation ◽  
Optimization Problem ◽  
Filter Design ◽  
Stop Band ◽  
Optimal Solution ◽  
Improved Genetic Algorithm ◽  
Global Optimal Solution ◽  
Prototype Filter ◽  
Global Optimal

A prototype filter design for FBMC/OQAM systems is proposed in this study. The influence of both the channel estimation and the stop-band energy is taken into account in this method. An efficient preamble structure is proposed to improve the performance of channel estimation and save the frequency spectral efficiency. The reciprocal of the signal-to-interference plus noise ratio (RSINR) is derived to measure the influence of the prototype filter on channel estimation. After that, the process of prototype filter design is formulated as an optimization problem with constraint on the RSINR. To accelerate the convergence and obtain global optimal solution, an improved genetic algorithm is proposed. Especially, the History Network and pruning operator are adopted in this improved genetic algorithm. Simulation results demonstrate the validity and efficiency of the prototype filter designed in this study.

scholarly journals A Shearlets-Based Method for Rain Removal from Single Images

2019 ◽  
Vol 9 (23) ◽  
pp. 5137 ◽  
Author(s):  
Guomin Sun ◽  
Jinsong Leng ◽  
Carlo Cattani
Keyword(s):  
Optimal Solution ◽  
Single Image ◽  
Split Bregman ◽  
Global Optimal Solution ◽  
Rain Removal ◽  
Rain Drops ◽  
Global Optimal ◽  
Removal Model ◽  
Split Bregman Algorithm ◽  
Sparse Priors

This work focuses on the problem of rain removal from a single image. The directional multilevel system, Shearlets, is used to describe the intrinsic directional and structure sparse priors of rain streaks and the background layer. In this paper, a Shearlets-based convex rain removal model is proposed, which involves three sparse regularizers: including the sparse regularizer of rain streaks and two sparse regularizers of the Shearlets transform of background layer in the rain drops’ direction and the Shearlets transform of rain streaks in the perpendicular direction. The split Bregman algorithm is utilized to solve the proposed convex optimization model, which ensures the global optimal solution. Comparison tests with three state-of-the-art methods are implemented on synthetic and real rainy images, which suggests that the proposed method is efficient both in rain removal and details preservation of the background layer.

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