scholarly journals Geometric branch-and-bound methods for constrained global optimization problems

2012 ◽  
Vol 57 (3) ◽  
pp. 771-782 ◽  
Author(s):  
Daniel Scholz
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Optimization Problems ◽  
Constrained Global Optimization ◽  
Branch And Bound Methods

scholarly journals BRANCH AND BOUND WITH SIMPLICIAL PARTITIONS FOR GLOBAL OPTIMIZATION

2008 ◽  
Vol 13 (1) ◽  
pp. 145-159 ◽  
Author(s):  
J. Žilinskas
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Linear Inequality ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Combinatorial Approach ◽  
Rectangular Shape ◽  
Linear Inequality Constraints ◽  
Advantages And Disadvantages ◽  
Branch And Bound Methods

Branch and bound methods for global optimization are considered in this paper. Advantages and disadvantages of simplicial partitions for branch and bound are shown. A new general combinatorial approach for vertex triangulation of hyper‐rectangular feasible regions is presented. Simplicial partitions may be used to vertex triangulate feasible regions of non rectangular shape defined by linear inequality constraints. Linear inequality constraints may be used to avoid symmetries in optimization problems.

scholarly journals A new auxiliary function approach for inequality constrained global optimization problems

2019 ◽  
Vol 9 (3) ◽  
pp. 31-38
Author(s):  
Nurullah Yilmaz ◽  
Ahmet Sahiner
Keyword(s):  
Global Optimization ◽  
Penalty Function ◽  
Optimization Problems ◽  
Auxiliary Function ◽  
Exact Penalty Function ◽  
Function Approach ◽  
Exact Penalty ◽  
Constrained Global Optimization ◽  
Constrained Optimization Problems ◽  
Smooth Exact Penalty Function

In this study, we deal with the nonlinear constrained global optimization problems. First, we introduce a new smooth exact penalty function for constrained optimization problems. We combine the exact penalty function with the auxiliary function in regard to constrained global optimization. We present a new auxiliary function approach and the adapted algorithm for solving  non-linear inequality constrained global optimization problems. Finally, we illustrate the efficiency of the algorithm on some numerical examples.

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