A computational study of active set strategies in nonlinear programming with linear constraints

1979 ◽  
Vol 16 (1) ◽  
pp. 81-97 ◽  
Author(s):  
Melanie L. Lenard
Keyword(s):  
Nonlinear Programming ◽  
Computational Study ◽  
Linear Constraints ◽  
Active Set ◽  
Active Set Strategies

A computational study of active-set logics for nonlinear programming

1985 ◽  
Vol 13 ◽  
pp. 157-170 ◽  
Author(s):  
Dongwon Rew ◽  
H.J Kelley ◽  
E.M Cliff
Keyword(s):  
Nonlinear Programming ◽  
Computational Study ◽  
Active Set

A Computational Study of Active-set Logics for Nonlinear Programming *

1985 ◽  
Vol 18 (2) ◽  
pp. 157-170
Author(s):  
Dongwon Rew ◽  
H.J. Kelley ◽  
E.M. Cliff
Keyword(s):  
Nonlinear Programming ◽  
Computational Study ◽  
Active Set

Active set strategies in an ellipsoid algorithm for nonlinear programming

2004 ◽  
Vol 31 (6) ◽  
pp. 941-962 ◽  
Author(s):  
Edgar K. Rugenstein ◽  
Michael Kupferschmid
Keyword(s):  
Nonlinear Programming ◽  
Ellipsoid Algorithm ◽  
Active Set ◽  
Active Set Strategies

Monotonicity and Active Set Strategies in Probabilistic Design Optimization

2005 ◽  
Author(s):  
Kuei-Yuan Chan ◽  
Steven J. Skerlos ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Computational Cost ◽  
Inequality Constraints ◽  
Probabilistic Constraints ◽  
Programming Algorithm ◽  
Probabilistic Design ◽  
Active Set ◽  
Probability Metrics ◽  
Active Set Strategies ◽  
Monotonicity Analysis

Probabilistic design optimization addresses the presence of uncertainty in design problems. Extensive studies on Reliability-Based Design Optimization (RBDO), i.e., problems with random variables and probabilistic constraints, have focused on improving computational efficiency of estimating values for the probabilistic functions. In the presence of many probabilistic inequality constraints, computational costs can be reduced if probabilistic values are computed only for constraints that are known to be active or likely active. This article presents an extension of monotonicity analysis concepts from deterministic problems to probabilistic ones, based on the fact that several probability metrics are monotonic transformations. These concepts can be used to construct active set strategies that reduce the computational cost associated with handling inequality constraints, similarly to the deterministic case. Such a strategy is presented as part of a sequential linear programming algorithm along with a numerical example.

Monotonicity and Active Set Strategies in Probabilistic Design Optimization

2006 ◽  
Vol 128 (4) ◽  
pp. 893-900 ◽  
Author(s):  
Kuei-Yuan Chan ◽  
Steven Skerlos ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Computational Cost ◽  
Inequality Constraints ◽  
Probabilistic Constraints ◽  
Programming Algorithm ◽  
Probabilistic Design ◽  
Active Set ◽  
Probability Metrics ◽  
Active Set Strategies ◽  
Monotonicity Analysis

Probabilistic design optimization addresses the presence of uncertainty in design problems. Extensive studies on reliability-based design optimization, i.e., problems with random variables and probabilistic constraints, have focused on improving computational efficiency of estimating values for the probabilistic functions. In the presence of many probabilistic inequality constraints, computational costs can be reduced if probabilistic values are computed only for constraints that are known to be active or likely active. This article presents an extension of monotonicity analysis concepts from deterministic problems to probabilistic ones, based on the fact that several probability metrics are monotonic transformations. These concepts can be used to construct active set strategies that reduce the computational cost associated with handling inequality constraints, similarly to the deterministic case. Such a strategy is presented as part of a sequential linear programming algorithm along with numerical examples.

scholarly journals Active‐Set Newton Methods and Partial Smoothness

2020 ◽  
Author(s):  
Adrian S. Lewis ◽  
Calvin Wylie
Keyword(s):  
Nonlinear Programming ◽  
Variational Inequalities ◽  
Finite Time ◽  
Optimization Algorithms ◽  
Newton Methods ◽  
Active Set ◽  
Local Algorithms ◽  
Partial Smoothness ◽  
Analogous Behavior ◽  
Partly Smooth

Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond optimization to systems involving partly smooth operators, and in particular to variational inequalities over partly smooth sets. As in classical nonlinear programming, such active‐set structure underlies the design of accelerated local algorithms of Newton type. We formalize this idea in broad generality as a simple linearization scheme for two intersecting manifolds.

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