scholarly journals On the applicability and solution of bilevel optimization models in transportation science: A study on the existence, stability and computation of optimal solutions to stochastic mathematical programs with equilibrium constraints

2008 ◽  
Vol 42 (10) ◽  
pp. 843-860 ◽  
Author(s):  
Michael Patriksson
Keyword(s):  
Bilevel Optimization ◽  
Optimization Models ◽  
Optimal Solutions ◽  
Equilibrium Constraints ◽  
Mathematical Programs

scholarly journals Neutrosophic Number Optimization Models and Their Application in the Practical Production Process

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Angyan Tu ◽  
Jun Ye ◽  
Bing Wang
Keyword(s):  
Production Process ◽  
Optimal Solution ◽  
Optimization Models ◽  
Optimal Solutions ◽  
Practical Applications ◽  
Linear And Nonlinear Programming ◽  
Constrained Conditions ◽  
Minimum Objective Function ◽  
Maximum Minimum ◽  
Neutrosophic Number

In order to simplify the complex calculation and solve the difficult solution problems of neutrosophic number optimization models (NNOMs) in the practical production process, this paper presents two methods to solve NNOMs, where Matlab built-in function “fmincon()” and neutrosophic number operations (NNOs) are used in indeterminate environments. Next, the two methods are applied to linear and nonlinear programming problems with neutrosophic number information to obtain the optimal solution of the maximum/minimum objective function under the constrained conditions of practical productions by neutrosophic number optimization programming (NNOP) examples. Finally, under indeterminate environments, the fit optimal solutions of the examples can also be achieved by using some specified indeterminate scales to fulfill some specified actual requirements. The NNOP methods can obtain the feasible and flexible optimal solutions and indicate the advantage of simple calculations in practical applications.

scholarly journals A note on the paper "Necessary and sufficient optimality conditions using convexifactors for mathematical programs with equilibrium constraints"

2021 ◽  
Author(s):  
Nazih Abderrazzak Gadhi
Keyword(s):  
Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Equilibrium Constraints ◽  
Mathematical Programs ◽  
Necessary And Sufficient

In this work, some counterexamples are given to refute some results in the paper by Kohli (RAIRO-Oper. Res. 53, 1617-1632, 2019). We correct the faulty in some of his results.

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