An infeasible active-set QP-free algorithm for general nonlinear programming

2016 ◽  
Vol 94 (5) ◽  
pp. 884-901 ◽  
Author(s):  
Hua Wang ◽  
Fuyao Liu ◽  
Chao Gu ◽  
Dingguo Pu
Keyword(s):  
Nonlinear Programming ◽  
Active Set ◽  
General Nonlinear Programming

scholarly journals Evolutionary Algorithms for Constrained Parameter Optimization Problems

1996 ◽  
Vol 4 (1) ◽  
pp. 1-32 ◽  
Author(s):  
Zbigniew Michalewicz ◽  
Marc Schoenauer
Keyword(s):  
Nonlinear Programming ◽  
Evolutionary Algorithms ◽  
Evolutionary Computation ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Optimization Techniques ◽  
Test Cases ◽  
Nonlinear Constraints ◽  
Nonlinear Programming Problem ◽  
General Nonlinear Programming

Evolutionary computation techniques have received a great deal of attention regarding their potential as optimization techniques for complex numerical functions. However, they have not produced a significant breakthrough in the area of nonlinear programming due to the fact that they have not addressed the issue of constraints in a systematic way. Only recently have several methods been proposed for handling nonlinear constraints by evolutionary algorithms for numerical optimization problems; however, these methods have several drawbacks, and the experimental results on many test cases have been disappointing. In this paper we (1) discuss difficulties connected with solving the general nonlinear programming problem; (2) survey several approaches that have emerged in the evolutionary computation community; and (3) provide a set of 11 interesting test cases that may serve as a handy reference for future methods.

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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