scholarly journals Probabilistic nonconvex constrained optimization with fixed number of function evaluations

2017 ◽  
Vol 113 (4) ◽  
pp. 719-741 ◽  
Author(s):  
Roger Ghanem ◽  
Christian Soize
Keyword(s):  
Constrained Optimization ◽  
Fixed Number ◽  
Nonconvex Constrained Optimization

scholarly journals Nonconvex constrained optimization by a filtering branch and bound

2020 ◽  
Author(s):  
Gabriele Eichfelder ◽  
Kathrin Klamroth ◽  
Julia Niebling
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Constrained Optimization Problem ◽  
Numerical Tests ◽  
Nonconvex Constrained Optimization ◽  
Objective Value ◽  
Feasible Solutions ◽  
Quality Guarantee ◽  
Single Objective

AbstractA major difficulty in optimization with nonconvex constraints is to find feasible solutions. As simple examples show, the $$\alpha $$ α BB-algorithm for single-objective optimization may fail to compute feasible solutions even though this algorithm is a popular method in global optimization. In this work, we introduce a filtering approach motivated by a multiobjective reformulation of the constrained optimization problem. Moreover, the multiobjective reformulation enables to identify the trade-off between constraint satisfaction and objective value which is also reflected in the quality guarantee. Numerical tests validate that we indeed can find feasible and often optimal solutions where the classical single-objective $$\alpha $$ α BB method fails, i.e., it terminates without ever finding a feasible solution.

scholarly journals Error Bounds and Finite Termination for Constrained Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wenling Zhao ◽  
Daojin Song ◽  
Bingzhuang Liu
Keyword(s):  
Constrained Optimization ◽  
Error Bound ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Merit Function ◽  
Global Error Bound ◽  
Constrained Optimization Problems ◽  
Nonconvex Constrained Optimization ◽  
Necessary And Sufficient

We present a global error bound for the projected gradient of nonconvex constrained optimization problems and a local error bound for the distance from a feasible solution to the optimal solution set of convex constrained optimization problems, by using the merit function involved in the sequential quadratic programming (SQP) method. For the solution sets (stationary points set andKKTpoints set) of nonconvex constrained optimization problems, we establish the definitions of generalized nondegeneration and generalized weak sharp minima. Based on the above, the necessary and sufficient conditions for a feasible solution of the nonconvex constrained optimization problems to terminate finitely at the two solutions are given, respectively. Accordingly, the results in this paper improve and popularize existing results known in the literature. Further, we utilize the global error bound for the projected gradient with the merit function being computed easily to describe these necessary and sufficient conditions.

scholarly journals A family of global convergent inexact secant methods for nonconvex constrained optimization

2018 ◽  
Vol 12 (2) ◽  
pp. 165-176
Author(s):  
Zhujun Wang ◽  
Li Cai ◽  
Zheng Peng
Keyword(s):  
Global Convergence ◽  
Constrained Optimization ◽  
Line Search ◽  
Merit Function ◽  
Exact Penalty ◽  
Search Technique ◽  
Nonconvex Constrained Optimization ◽  
Secant Methods ◽  
Armijo Line Search ◽  
Line Search Technique

We present a family of new inexact secant methods in association with Armijo line search technique for solving nonconvex constrained optimization. Different from the existing inexact secant methods, the algorithms proposed in this paper need not compute exact directions. By adopting the nonsmooth exact penalty function as the merit function, the global convergence of the proposed algorithms is established under some reasonable conditions. Some numerical results indicate that the proposed algorithms are both feasible and effective.

scholarly journals A Hybrid Epigraph Directions Method for Nonsmooth and Nonconvex Constrained Optimization via Generalized Augmented Lagrangian Duality and a Genetic Algorithm

2018 ◽  
Vol 2018 ◽  
pp. 1-21
Author(s):  
Wilhelm P. Freire ◽  
Afonso C. C. Lemonge ◽  
Tales L. Fonseca ◽  
Hernando J. R. Franco
Keyword(s):  
Genetic Algorithm ◽  
Constrained Optimization ◽  
Augmented Lagrangian ◽  
Dual Problem ◽  
Optimization Problems ◽  
Lagrangian Duality ◽  
Dual Function ◽  
Constrained Optimization Problems ◽  
Nonconvex Constrained Optimization ◽  
Nonsmooth And Nonconvex Optimization

The Interior Epigraph Directions (IED) method for solving constrained nonsmooth and nonconvex optimization problem via Generalized Augmented Lagrangian Duality considers the dual problem induced by a Generalized Augmented Lagrangian Duality scheme and obtains the primal solution by generating a sequence of iterates in the interior of the epigraph of the dual function. In this approach, the value of the dual function at some point in the dual space is given by minimizing the Lagrangian. The first version of the IED method uses the Matlab routine fminsearch for this minimization. The second version uses NFDNA, a tailored algorithm for unconstrained, nonsmooth and nonconvex problems. However, the results obtained with fminsearch and NFDNA were not satisfactory. The current version of the IED method, presented in this work, employs a Genetic Algorithm, which is free of any strategy to handle the constraints, a difficult task when a metaheuristic, such as GA, is applied alone to solve constrained optimization problems. Two sets of constrained optimization problems from mathematics and mechanical engineering were solved and compared with literature. It is shown that the proposed hybrid algorithm is able to solve problems where fminsearch and NFDNA fail.

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