An improved infeasible SSLE method for constrained optimization without strict complementarity

2013 ◽  
Vol 40 (5) ◽  
pp. 1506-1515 ◽  
Author(s):  
Wei-Xin Cheng ◽  
Chong-Chao Huang ◽  
Jin-Bao Jian
Keyword(s):  
Constrained Optimization ◽  
Strict Complementarity

The Rate of Convergence of a NLM Based on F–B NCP for Constrained Optimization Problems Without Strict Complementarity

2015 ◽  
Vol 32 (03) ◽  
pp. 1550012 ◽  
Author(s):  
Suxiang He ◽  
Liwei Zhang ◽  
Jie Zhang
Keyword(s):  
Constrained Optimization ◽  
Rate Of Convergence ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Augmented Lagrangian Method ◽  
Inequality Constraints ◽  
Constrained Optimization Problems ◽  
Strict Complementarity ◽  
Linear Rate ◽  
Nonlinear Lagrangian

It is well-known that the linear rate of convergence can be established for the classical augmented Lagrangian method for constrained optimization problems without strict complementarity. Whether this result is still valid for other nonlinear Lagrangian methods (NLM) is an interesting problem. This paper proposes a nonlinear Lagrangian function based on Fischer–Burmeister (F–B) nonlinear complimentarity problem (NCP) function for constrained optimization problems. The rate of convergence of this NLM is analyzed under the linear independent constraint qualification and the strong second-order sufficient condition without strict complementarity when subproblems are assumed to be solved exactly and inexactly, respectively. Interestingly, it is demonstrated that the Lagrange multipliers associating with inactive inequality constraints at the local minimum point converge to zeros superlinearly. Several illustrative examples are reported to show the behavior of the NLM.

Constrained Optimization for Portfolio Construction

CFA Digest ◽  
2012 ◽  
Vol 42 (3) ◽  
pp. 148-150
Author(s):  
Gregory G. Gocek
Keyword(s):  
Constrained Optimization ◽  
Portfolio Construction
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