A decomposition algorithm for nonlinear inseparable hierarchical optimization problems

1993 ◽  
Vol 5 (3) ◽  
pp. 184-189 ◽  
Author(s):  
G. Feng
Keyword(s):  
Optimization Problems ◽  
Decomposition Algorithm ◽  
Hierarchical Optimization ◽  
Hierarchical Optimization Problems

Subgradient algorithm for split hierarchical optimization problems

2018 ◽  
Vol 34 (3) ◽  
pp. 391-399
Author(s):  
NIMIT NIMANA ◽  
◽  
NARIN PETROT ◽  
◽  
Keyword(s):  
Hilbert Spaces ◽  
Optimization Problems ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Hierarchical Optimization ◽  
Convergence Results ◽  
Hierarchical Optimization Problems ◽  
Subgradient Algorithm ◽  
The Split Feasibility Problem ◽  
Split Feasibility

In this paper we emphasize a split type problem of some integrating ideas of the split feasibility problem and the hierarchical optimization problem. Working on real Hilbert spaces, we propose a subgradient algorithm for approximating a solution of the introduced problem. We discuss its convergence results and present a numerical example.

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.

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