A new algorithm for highly curved constrained optimisation

1987 ◽  
pp. 139-154 ◽  
Author(s):  
Z. A. Maany
Keyword(s):  
Constrained Optimisation

scholarly journals Nonsmooth invexity

1990 ◽  
Vol 42 (3) ◽  
pp. 437-446 ◽  
Author(s):  
Thomas W. Reiland
Keyword(s):  
Lipschitz Functions ◽  
Constrained Optimisation ◽  
Nondifferentiable Functions ◽  
Analytic Tool

The concept of invexity is extended to nondifferentiable functions. Characterisations of nonsmooth invexity are derived as well as results in unconstrained and constrained optimisation and duality. The principal analytic tool is the generalised gradient of Clarke for Lipschitz functions.

scholarly journals Stabilised explicit Adams-type methods

2021 ◽  
pp. 82-98
Author(s):  
Vasily I. Repnikov ◽  
Boris V. Faleichik ◽  
Andrew V. Moisa
Keyword(s):  
Numerical Experiments ◽  
Step Method ◽  
Type Method ◽  
Constrained Optimisation ◽  
First Order ◽  
Error Constant ◽  
Stability Intervals ◽  
Multi Step Methods ◽  
First Order Methods ◽  
Accuracy And Stability

In this work we present explicit Adams-type multi-step methods with extended stability intervals, which are analogous to the stabilised Chebyshev Runge – Kutta methods. It is proved that for any k ≥ 1 there exists an explicit k-step Adams-type method of order one with stability interval of length 2k. The first order methods have remarkably simple expressions for their coefficients and error constant. A damped modification of these methods is derived. In the general case, to construct a k-step method of order p it is necessary to solve a constrained optimisation problem in which the objective function and p constraints are second degree polynomials in k variables. We calculate higher-order methods up to order six numerically and perform some numerical experiments to confirm the accuracy and stability of the methods.

A Distributed Approach for Accessibility and Maintainability Check With a Manikin

1999 ◽  
Author(s):  
Patrick Chedmail ◽  
Christophe Le Roy
Keyword(s):  
Virtual Reality ◽  
Original Method ◽  
Direct Manipulation ◽  
Agent Architecture ◽  
Constrained Optimisation ◽  
Cluttered Environment ◽  
Distributed Approach ◽  
Multi Agent ◽  
The One ◽  
Algorithmic Approaches

Abstract The validation of the accessibility, maintainability, mounting/dismantle simulation in a cluttered environment is a key problem during the design process of a mechanical system. On the one hand research in path planning lead to automatic trajectory definition. These systems are really efficient for simple problems. On the other hand direct manipulation is possible thanks to robotic CAD systems. Another direct manipulation is possible with common virtual reality tools that allow the designer immersion in a whole mechanical environment. In such an environment the designer can handle an object in order to check its accessibility. Thanks to the use of a multi-agent architecture we greatly improve the effectiveness of virtual reality tools while coupling algorithmic approaches and direct manipulation. This original method is a solution of a multi-criteria constrained optimisation problem. Theoretical and practical aspects are presented.

scholarly journals STRATEGIES FOR CONSTRAINED OPTIMISATION

ICGA Journal ◽  
2000 ◽  
Vol 23 (1) ◽  
pp. 9-20 ◽  
Author(s):  
G. McC. Haworth
Keyword(s):  
Constrained Optimisation
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