scholarly journals Trust-region problems with linear inequality constraints: exact SDP relaxation, global optimality and robust optimization

2013 ◽  
Vol 147 (1-2) ◽  
pp. 171-206 ◽  
Author(s):  
V. Jeyakumar ◽  
G. Y. Li
2010 ◽  
Vol 27 (01) ◽  
pp. 85-101
Author(s):  
HAI-JUN WANG ◽  
QIN NI

A new method of moving asymptotes for large scale minimization subject to linear inequality constraints is discussed in this paper. In each step of the iterative process, a descend direction is obtained by solving a convex separable subproblem with dual technique. The new rules for controlling the asymptotes parameters are designed by the trust region radius and some approximation properties such that the global convergence of the new method are obtained. The numerical results show that the new method may be capable of processing some large scale problems.


Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1369
Author(s):  
Temadher A. Almaadeed ◽  
Akram Taati ◽  
Maziar Salahi ◽  
Abdelouahed Hamdi

In this paper, we study the problem of minimizing a general quadratic function subject to a quadratic inequality constraint with a fixed number of additional linear inequality constraints. Under a regularity condition, we first introduce two convex quadratic relaxations (CQRs), under two different conditions, that are minimizing a linear objective function over two convex quadratic constraints with additional linear inequality constraints. Then, we discuss cases where the CQRs return the optimal solution of the problem, revealing new conditions under which the underlying problem admits strong Lagrangian duality and enjoys exact semidefinite optimization relaxation. Finally, under the given sufficient conditions, we present necessary and sufficient conditions for global optimality of the problem and obtain a form of S-lemma for a system of two quadratic and a fixed number of linear inequalities.


2018 ◽  
Vol 224 ◽  
pp. 01112
Author(s):  
Dmitriy L. Skuratov ◽  
Dmitriy G. Fedorov ◽  
Dmitriy V. Evdokimov

A mathematical model is presented for determining the rational machining conditions for flat grinding operations by the rim of a wheel on machines with a rectangular table consisting of a linear objective function and linear inequality constraints. As the objective function, the equation, determining the main machining time, was used. And constraints which are related to the functional parameters and parameters determining the machining quality and the kinematic capabilities of the machine were used as inequality constraints.


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