Differential Evolution for linear equality constraint satisfaction via unconstrained search in the null space

2021 ◽  
Author(s):  
Jaqueline S. Angelo ◽  
Helio J. C. Barbosa ◽  
Heder S. Bernardino
Keyword(s):  
Differential Evolution ◽  
Constraint Satisfaction ◽  
Null Space ◽  
Equality Constraint ◽  
Linear Equality ◽  
Linear Equality Constraint

scholarly journals An efficient method for minimizing a convex separable logarithmic function subject to a convex inequality constraint or linear equality constraint

2006 ◽  
Vol 2006 ◽  
pp. 1-19 ◽  
Author(s):  
Stefan M. Stefanov
Keyword(s):  
Inequality Constraint ◽  
Point Of View ◽  
Equality Constraint ◽  
Polynomial Algorithms ◽  
Logarithmic Function ◽  
Planning And Scheduling ◽  
Linear Equality ◽  
Convex Inequality ◽  
Linear Equality Constraint ◽  
Mathematical Programming Problems

We consider the problem of minimizing a convex separable logarithmic function over a region defined by a convex inequality constraint or linear equality constraint, and two-sided bounds on the variables (box constraints). Such problems are interesting from both theoretical and practical point of view because they arise in some mathematical programming problems as well as in various practical problems such as problems of production planning and scheduling, allocation of resources, decision making, facility location problems, and so forth. Polynomial algorithms are proposed for solving problems of this form and their convergence is proved. Some examples and results of numerical experiments are also presented.

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