A new approach for computing consistent initial values and Taylor coefficients for DAEs using projector-based constrained optimization

2017 ◽  
Vol 78 (2) ◽  
pp. 355-377 ◽  
Author(s):  
Diana Estévez Schwarz ◽  
René Lamour
Keyword(s):  
Constrained Optimization ◽  
New Approach ◽  
Taylor Coefficients ◽  
Initial Values ◽  
Consistent Initial Values

scholarly journals Projected explicit and implicit Taylor series methods for DAEs

2021 ◽  
Author(s):  
Diana Estévez Schwarz ◽  
René Lamour
Keyword(s):  
Taylor Series ◽  
Multibody Systems ◽  
Optimization Problem ◽  
Automatic Differentiation ◽  
Taylor Coefficients ◽  
Integration Schemes ◽  
Consistent Initial Values ◽  
Taylor Series Methods ◽  
Systems Simulation ◽  
Derivative Array

AbstractThe recently developed new algorithm for computing consistent initial values and Taylor coefficients for DAEs using projector-based constrained optimization opens new possibilities to apply Taylor series integration methods. In this paper, we show how corresponding projected explicit and implicit Taylor series methods can be adapted to DAEs of arbitrary index. Owing to our formulation as a projected optimization problem constrained by the derivative array, no explicit description of the inherent dynamics is necessary, and various Taylor integration schemes can be defined in a general framework. In particular, we address higher-order Padé methods that stand out due to their stability. We further discuss several aspects of our prototype implemented in Python using Automatic Differentiation. The methods have been successfully tested on examples arising from multibody systems simulation and a higher-index DAE benchmark arising from servo-constraint problems.

Computation of Consistent Initial Values for Nonlinear Index 3 DAEs

2007 ◽  
Author(s):  
René Lamour ◽  
Francesca Mazzia ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Initial Values ◽  
Consistent Initial Values ◽  
Nonlinear Index

Motion planning of redundant robot manipulators using constrained optimization: A parallel approach

1998 ◽  
Vol 212 (4) ◽  
pp. 281-292 ◽  
Author(s):  
C-L Chen ◽  
C-J Lin
Keyword(s):  
Motion Planning ◽  
Constrained Optimization ◽  
Tracking Error ◽  
Position Angle ◽  
Sampling Interval ◽  
Maximum Speed ◽  
Redundancy Resolution ◽  
Tracking Errors ◽  
New Approach ◽  
Resolution Problem

A redundant manipulator can achieve a principal task and additional tasks by utilizing the degrees of redundancy. In the present paper, the redundancy resolution problem is formulated as a local equality constrained optimization problem. A motion planning solution corresponding to a design objective is then obtained using a new approach, called the perturbation method. In contrast to conventional approaches, the inverse of the Jacobian matrix is not required in the method proposed. Tracking errors can be bounded by a permissible zone, which is a function of normal tracking error and a safety factor. Positioning of the end effector within the permissible zone is satisfactory for the completion of any given step and signals the beginning of the next step. The position angle change of each joint is also bounded in each sampling interval as a function of robot maximum speed. Computer simulations written in the parallel processing language occam and computed on a transputer-based computation network are used to study the behaviour of the method proposed. Results validate the approach.

scholarly journals Sequential optimality conditions for cardinality-constrained optimization problems with applications

2021 ◽  
Author(s):  
Christian Kanzow ◽  
Andreas B. Raharja ◽  
Alexandra Schwartz
Keyword(s):  
Constrained Optimization ◽  
Optimality Conditions ◽  
Optimality Condition ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Local Minimizer ◽  
Constrained Optimization Problems ◽  
New Approach ◽  
Mathematical Programs ◽  
Sequential Optimality Conditions

AbstractRecently, a new approach to tackle cardinality-constrained optimization problems based on a continuous reformulation of the problem was proposed. Following this approach, we derive a problem-tailored sequential optimality condition, which is satisfied at every local minimizer without requiring any constraint qualification. We relate this condition to an existing M-type stationary concept by introducing a weak sequential constraint qualification based on a cone-continuity property. Finally, we present two algorithmic applications: We improve existing results for a known regularization method by proving that it generates limit points satisfying the aforementioned optimality conditions even if the subproblems are only solved inexactly. And we show that, under a suitable Kurdyka–Łojasiewicz-type assumption, any limit point of a standard (safeguarded) multiplier penalty method applied directly to the reformulated problem also satisfies the optimality condition. These results are stronger than corresponding ones known for the related class of mathematical programs with complementarity constraints.

scholarly journals Ghost Penalties in Nonconvex Constrained Optimization: Diminishing Stepsizes and Iteration Complexity

2021 ◽  
Author(s):  
Francisco Facchinei ◽  
Vyacheslav Kungurtsev ◽  
Lorenzo Lampariello ◽  
Gesualdo Scutari
Keyword(s):  
Theoretical Analysis ◽  
Constrained Optimization ◽  
Sequential Quadratic Programming ◽  
Optimization Problems ◽  
Penalty Functions ◽  
Stationary Points ◽  
Iteration Complexity ◽  
Constrained Optimization Problems ◽  
New Approach ◽  
Nonconvex Constrained Optimization

We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. We make use of classical penalty functions in an unconventional way, in that penalty functions only enter in the theoretical analysis of convergence while the algorithm itself is penalty free. Based on this idea, we are able to establish several new results, including the first general analysis for diminishing stepsize methods in nonconvex, constrained optimization, showing convergence to generalized stationary points, and a complexity study for sequential quadratic programming–type algorithms.

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