Alternating Direction Method of Solving Nonlinear Programming with Inequality Constrained

2014 ◽  
Vol 651-653 ◽  
pp. 2107-2111
Author(s):  
Ai Fen Feng ◽  
Li Ming Zhang ◽  
Zhen Xia Xue
Keyword(s):  
Nonlinear Programming ◽  
Lagrange Function ◽  
Inequality Constraints ◽  
Alternating Direction Method ◽  
New Class ◽  
Ncp Function ◽  
Kkt Point ◽  
Alternating Direction ◽  
Local Point ◽  
Unconstrained Problem

This paper, a new class of augmented Lagrange functions with the new NCP function is proposed for the minimization of a smooth function subject to inequality constraints. Under some conditions, we prove of the equivalences of the KKT point and local point and globe point between primal constrained nonlinear programming problem and the new unconstrained problem. By the character of augmented Lagrange function, the algorithm which uses alternating direction method is constructed and proved convergence.

The Engineering Application of Improved Alternating Direction Method for Solving Power Systems Multi-Area Dispatch Problem

2015 ◽  
Vol 740 ◽  
pp. 929-932
Author(s):  
Ya Ming Ren ◽  
Shu Min Fei ◽  
Hai Kun Wei
Keyword(s):  
Power Systems ◽  
Economic Dispatch ◽  
Engineering Application ◽  
Inequality Constraints ◽  
Alternating Direction Method ◽  
Penalty Parameter ◽  
Alternating Direction ◽  
Equality And Inequality Constraints ◽  
Convergence Performance ◽  
Consistency Constraint

The alternating direction method has been widespread used to solve multi-area economic dispatch problem. Compared with traditional centered economic dispatch, alternating direction method divides centered optimal problem into completely independent sub-problems while the corresponding equality and inequality constraints are satisfied. However, plenty of applications show that the choice of penalty parameter for the consistency constraint has an important influence on the convergence performance of alternating direction method. In this paper, we proposed a novel improved alternating direction method. To be more exact, the key is to adjust penalty parameter based on iterative information of alternating direction method. Numerical results illustrate the proposed method has better stability in convergence.

scholarly journals MADAM: a parallel exact solver for max-cut based on semidefinite programming and ADMM

2021 ◽  
Vol 80 (2) ◽  
pp. 347-375
Author(s):  
Timotej Hrga ◽  
Janez Povh
Keyword(s):  
State Of The Art ◽  
Inequality Constraints ◽  
Alternating Direction Method ◽  
Dual Variable ◽  
Maximum Weight ◽  
New Approach ◽  
Parallel Solver ◽  
Alternating Direction ◽  
Computationally Expensive ◽  
Serial Algorithm

AbstractWe present , a parallel semidefinite-based exact solver for Max-Cut, a problem of finding the cut with the maximum weight in a given graph. The algorithm uses the branch and bound paradigm that applies the alternating direction method of multipliers as the bounding routine to solve the basic semidefinite relaxation strengthened by a subset of hypermetric inequalities. The benefit of the new approach is a less computationally expensive update rule for the dual variable with respect to the inequality constraints. We provide a theoretical convergence of the algorithm as well as extensive computational experiments with this method, to show that our algorithm outperforms state-of-the-art approaches. Furthermore, by combining algorithmic ingredients from the serial algorithm, we develop an efficient distributed parallel solver based on MPI.

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