Strong Stationarity for Optimization Problems with Complementarity Constraints in Absence of Polyhedricity

2016 ◽  
Vol 25 (1) ◽  
pp. 133-175 ◽  
Author(s):  
Gerd Wachsmuth
Keyword(s):  
Optimization Problems ◽  
Complementarity Constraints ◽  
Strong Stationarity

A Regularized Inexact Penalty Decomposition Algorithm for Multidisciplinary Design Optimization Problems With Complementarity Constraints

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Shen Lu ◽  
Harrison M. Kim
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Original Problem ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Decomposition Algorithm ◽  
Multidisciplinary Design ◽  
Stationary Points ◽  
Complementarity Constraints ◽  
Regularization Technique

Economic and physical considerations often lead to equilibrium problems in multidisciplinary design optimization (MDO), which can be captured by MDO problems with complementarity constraints (MDO-CC)—a newly emerging class of problem. Due to the ill-posedness associated with the complementarity constraints, many existing MDO methods may have numerical difficulties solving this class of problem. In this paper, we propose a new decomposition algorithm for the MDO-CC based on the regularization technique and inexact penalty decomposition. The algorithm is presented such that existing proofs can be extended, under certain assumptions, to show that it converges to stationary points of the original problem and that it converges locally at a superlinear rate. Numerical computation with an engineering design example and several analytical example problems shows promising results with convergence to the all-in-one solution.

scholarly journals Relations between Abs-Normal NLPs and MPCCs. Part 1: Strong Constraint Qualifications

2021 ◽  
Vol Volume 2 (Original research articles>) ◽  
Author(s):  
Lisa C. Hegerhorst-Schultchen ◽  
Christian Kirches ◽  
Marc C. Steinbach
Keyword(s):  
Normal Form ◽  
Linear Independence ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Inequality Constraints ◽  
Strong Constraint ◽  
Strong Stationarity ◽  
Ongoing Effort ◽  
Equality And Inequality Constraints ◽  
Smooth Optimization

This work is part of an ongoing effort of comparing non-smooth optimization problems in abs-normal form to MPCCs. We study the general abs-normal NLP with equality and inequality constraints in relation to an equivalent MPCC reformulation. We show that kink qualifications and MPCC constraint qualifications of linear independence type and Mangasarian-Fromovitz type are equivalent. Then we consider strong stationarity concepts with first and second order optimality conditions, which again turn out to be equivalent for the two problem classes. Throughout we also consider specific slack reformulations suggested in [9], which preserve constraint qualifications of linear independence type but not of Mangasarian-Fromovitz type.

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