Template-Based Monocular 3D Recovery of Elastic Shapes Using Lagrangian Multipliers

2017 ◽  
Author(s):  
Nazim Haouchine ◽  
Stephane Cotin
Keyword(s):  
Lagrangian Multipliers ◽  
Elastic Shapes

The boundary element method with Lagrangian multipliers

2008 ◽  
Vol 25 (6) ◽  
pp. 1303-1319 ◽  
Author(s):  
Gabriel N. Gatica ◽  
Martin Healey ◽  
Norbert Heuer
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Lagrangian Multipliers ◽  
Element Method

Correspondence. Dynamic Programming and Lagrangian Multipliers

1965 ◽  
Vol 4 (4) ◽  
pp. 488-490 ◽  
Author(s):  
N. V. Junnarkar ◽  
S. M. Roberts
Keyword(s):  
Dynamic Programming ◽  
Lagrangian Multipliers

scholarly journals Joint 3-D Positioning and Power Allocation for UAV Relay Aided by Geographic Information

2021 ◽  
Author(s):  
Pengfei Yi ◽  
Liang Zhu ◽  
Lipeng Zhu ◽  
Zhenyu Xiao
Keyword(s):  
Power Allocation ◽  
Upper Bound ◽  
Three Dimensional ◽  
Geographic Information ◽  
Base Station ◽  
Lagrangian Multipliers ◽  
Loop Optimization ◽  
Convex Problem ◽  
Communication Links ◽  
Minimum Capacity

<div>In this paper, we study to employ geographic information to address the blockage problem of air-to-ground links between UAV and terrestrial nodes. In particular, a UAV relay is deployed to establish communication links from a ground base station to multiple ground users. To improve communication capacity, we fifirst model the blockage effect caused by buildings according to the three-dimensional (3-D) geographic information. Then, an optimization problem is formulated to maximize the minimum capacity among users by jointly optimizing the 3-D position and power allocation of the UAV relay, under the constraints of link capacity, maximum transmit power, and blockage. To solve this complex non-convex problem, a two-loop optimization framework is developed based on Lagrangian relaxation. The outer-loop aims to obtain proper Lagrangian multipliers to ensure the solution of the Lagrangian problem converge to the tightest upper bound on the original problem. The inner-loop solves the Lagrangian problem by applying the block coordinate descent (BCD) and successive convex approximation (SCA) techniques, where UAV 3-D positioning and power allocation are alternately optimized in each iteration. Simulation results confifirm that the proposed solution signifificantly outperforms two benchmark schemes and achieves a performance close to the upper bound on the UAV relay system.</div>

Combinatorial reverse auction based on revelation of Lagrangian multipliers

2010 ◽  
Vol 48 (2) ◽  
pp. 323-330 ◽  
Author(s):  
Fu-Shiung Hsieh
Keyword(s):  
Reverse Auction ◽  
Lagrangian Multipliers

A New Constrained Shape Deformation Operator With Applications in Footwear Design

2008 ◽  
Author(s):  
Ying Xu ◽  
Ajay Joneja
Keyword(s):  
Numerical Methods ◽  
Optimization Problem ◽  
Shape Change ◽  
Geometric Approach ◽  
Shape Deformation ◽  
Uzawa Method ◽  
Constrained Optimization Problem ◽  
Integral Property ◽  
Lagrangian Multipliers ◽  
Footwear Design

In this paper, we address a problem that arises in several engineering applications: the deformation of a curve with constraints on its length. Since length is an integral property, typically computed by numerical methods, therefore implementing such shape change operations is non trivial. Recently some researchers have attempted to solve such problems for multi-resolution representations of curves. However, we take a differential geometric approach. The modification problem is formulated as constrained optimization problem, which is subsequently converted to an unconstrained min-max problem using Lagrangian multipliers. This problem is solved using the Uzawa method. The approach is implemented in MATLAB™, and some examples are presented in the paper.

Unilateral Impact and Contact of Elastic Structures Using Lagrangian Multipliers

2011 ◽  
Author(s):  
Sebastian Tatzko
Keyword(s):  
Equations Of Motion ◽  
Structural Equations ◽  
Contact Forces ◽  
Integration Scheme ◽  
Lagrangian Multiplier ◽  
Elastic Structures ◽  
Lagrangian Multipliers ◽  
Linear Elastic ◽  
Time Stepping ◽  
Numerical Effort

This paper deals with linear elastic structures exposed to impact and contact phenomena. Within a time stepping integration scheme contact forces are computed with a Lagrangian multiplier approach. The main focus is turned on a simplified solving method of the linear complementarity problem for the frictionless contact. Numerical effort is reduced by applying a Craig-Bampton transformation to the structural equations of motion.

scholarly journals Exact strip postbuckling analysis of composite plates under compression and shear

2019 ◽  
Vol 123 (1263) ◽  
pp. 658-677
Author(s):  
K. Zhao ◽  
D. Kennedy ◽  
C.A. Featherston
Keyword(s):  
Finite Element ◽  
Composite Plates ◽  
Mode Shapes ◽  
Computational Time ◽  
Shear Load ◽  
Element Analysis ◽  
Lagrangian Multipliers ◽  
Buckling Loads ◽  
Finite Strip ◽  
Out Of Plane

ABSTRACTStiffened wing and fuselage panels often have a postbuckling reserve of strength, enabling them to carry loads far in excess of their critical buckling loads. Therefore allowing for postbuckling in design can reduce their weight, hence reducing fuel consumption and environmental impact. The present paper extends the postbuckling analysis in the exact strip software VICONOPT to more accurately reflect the skewed mode shapes arising from shear load and anisotropy. Such mode shapes are represented by a series of sinusoidal responses with different half-wavelengths which are coupled together using Lagrangian multipliers to enforce the boundary conditions. In postbuckling analysis the in-plane deflections involve responses with additional half-wavelengths which are absent from the out-of-plane deflection series. Numerical results are presented and compared with finite element analysis for validation. The present analysis gives close results compared to the finite element and finite strip methods and saves computational time significantly.

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