An efficient algorithm for solving a maximization problem under linear and quadratic inequality constraints

2002 ◽  
Author(s):  
G. Antonelli ◽  
S. Chiaverini ◽  
G. Fusco
Keyword(s):  
Efficient Algorithm ◽  
Inequality Constraints ◽  
Maximization Problem ◽  
Quadratic Inequality ◽  
Quadratic Inequality Constraints

scholarly journals Set-Membership Filtering for Nonlinear Dynamic Systems With Quadratic Inequality Constraints

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 13375-13386
Author(s):  
Xiaowei Li ◽  
Xuedong Yuan ◽  
Fanqin Meng ◽  
Yiwei Liao ◽  
Haiqi Liu ◽  
...  
Keyword(s):  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Inequality Constraints ◽  
Nonlinear Dynamic Systems ◽  
Quadratic Inequality ◽  
Set Membership ◽  
Quadratic Inequality Constraints

Resolving kinematic redundancy of a robot using a quadratically constrained optimization technique

Robotica ◽  
1999 ◽  
Vol 17 (5) ◽  
pp. 503-511 ◽  
Author(s):  
Woong Kwon ◽  
Beom Hee Lee ◽  
Myoung Hwan Choi
Keyword(s):  
Constrained Optimization ◽  
Optimization Technique ◽  
Inequality Constraints ◽  
Redundancy Resolution ◽  
Kinematic Redundancy ◽  
Problem Size ◽  
Physical Constraints ◽  
Quadratic Inequality ◽  
Quadratic Inequality Constraints ◽  
Quadratically Constrained

The constraints on the physical limit should be considered in a kinematic redundancy resolution problem of a robot. This paper proposes a new optimization scheme to resolve kinematic redundancy of the robot while considering physical constraints. In the proposed scheme, quadratic inequality constraints are used in place of linear inequality constraints, thus a quadratically constrained optimization technique is applied to resolve the redundancy. It is shown that the use of quadratic inequality constraints considerably reduces the number of constraints. Therefore, the proposed method reduces the problem size considerably and makes the problem simple resulting in computational efficiency. A numerical example of a 4-link planar redundant robot is included to demonstrate the efficiency of the proposed optimization technique. In this example, simulation results using the proposed method and another well-known method are compared and discussed.

Constrained Optimization Shooting Method for Predicting the Periodic Solutions of Nonlinear System

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
Haitao Liao
Keyword(s):  
Nonlinear System ◽  
Shooting Method ◽  
Continuation Method ◽  
Inequality Constraints ◽  
Original Method ◽  
Maximization Problem ◽  
Numerical Examples ◽  
Equality And Inequality Constraints ◽  
Parameter Continuation ◽  
Nonlinear Equality

An original method for calculating the maximum vibration amplitude of the periodic solution of a nonlinear system is presented. The problem of determining the worst maximum vibration is transformed into a nonlinear optimization problem. The shooting method and the Floquet theory are selected to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the effectiveness and ability of the proposed approach are illustrated through two numerical examples. Numerical examples show that the proposed method can give results with higher accuracy as compared with numerical results obtained by a parameter continuation method and the ability of the present method is also demonstrated.

scholarly journals Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Haitao Liao
Keyword(s):  
Limit Cycle ◽  
Harmonic Balance Method ◽  
Inequality Constraints ◽  
Maximization Problem ◽  
Limit Cycle Oscillation ◽  
Structural Parameter ◽  
Limit Cycle Oscillations ◽  
Aeroelastic System ◽  
Equality And Inequality Constraints ◽  
The Stability

In order to calculate the limit cycle oscillations and bifurcations of nonlinear aeroelastic system, the problem of finding periodic solutions with maximum vibration amplitude is transformed into a nonlinear optimization problem. An algebraic system of equations obtained by the harmonic balance method and the stability condition derived from the Floquet theory are used to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated, and the effects of structural parameter uncertainty on the limit cycle oscillations and bifurcations of an airfoil with multiple nonlinearities are studied. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

Mode Shape Expansion Techniques for Model Error Localization and Damage Detection

1995 ◽  
Author(s):  
Marie B. Levine-West ◽  
Mark H. Milman
Keyword(s):  
Mode Shape ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Model Error ◽  
Analytical Models ◽  
Mode Shapes ◽  
Orthogonal Projections ◽  
Modal Expansion ◽  
Expansion Technique ◽  
Quadratic Inequality Constraints

Abstract Several methods for mode shape expansion are investigated. The most popular methods use the dynamic equations of motions to obtain direct solutions, or use orthogonal projections. Both approaches can also be formulated as constrained optimization problems. To account for uncertainties in the measurements and in the prediction, a new expansion technique based on least squares minimization with quadratic inequality constraints (LSQI) is proposed. Each modal expansion technique is evaluated with experimental data obtained on the Micro-Precision Interferometer testbed, using both the pre-test and updated analytical models. The robustness of these methods is verified with respect to measurement noise and model error. It is shown that the proposed LSQI method has the best performance and can reliably predict mode shapes, and can be used to locate damage elements, even in very adverse situations. A new LSQI algorithm is also proposed which significantly decreases the solution time.

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