A feasible directions method for nonsmooth convex optimization

Herskovits, José; Freire, Wilhelm P.; Fo, Mario Tanaka; Canelas, Alfredo

doi:10.1007/s00158-011-0634-y

Cited by 10 publications

(6 citation statements)

References 26 publications

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“…Takezawa et al 18) and Brittain et al 5) solved problem (10) and problem (13), respectively, numerically and reported that the obtained optimal solutions have simple maximum eigenvalues. In contrast, Herskovits et al 11) found an optimal solution with fivefold maximum eigenvalue by using their algorithm for nonsmooth convex optimization. This section shows that, for truss structures, a series of simple problem instances can be constructed so that multiplicity of the optimal solution increases as the problem size increases.…”

Section: On Multiplicity Of Eigenvaluesmentioning

confidence: 97%

A Note on Formulations of Robust Compliance Optimization Under Uncertain Loads

Kanno

2015

Transactions of AIJ

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Several formulations are known for robust compliance optimization of structures subjected to uncertain static external loads.Aiming at providing clear perspective of the problem, this paper establishes connection between three formulations: a semidefinite programming formulation, a formulation as minimization of the maximum eigenvalue of a symmetric matrix, and a formulation using a generalized eigenvalue problem. Equivalence of these formulations is shown by using a fundamental property of the Schur complement of a symmetric positive semidefinite matrix. A series of numerical examples is presented to show that an optimal solution of the robust compliance optimization problem can possibly have eigenvalues of large multiplicity.

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Section: On Multiplicity Of Eigenvaluesmentioning

confidence: 97%

A Note on Formulations of Robust Compliance Optimization Under Uncertain Loads

Kanno

2015

Transactions of AIJ

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“…These are the main ideas from NFDA; we need to understand the IED algorithm. For more on NFDA, see [9,10].…”

Section: Nfda For Convex Problemsmentioning

confidence: 99%

“…The IED method [1] combines the Nonsmooth Feasible Directions Algorithm (NFDA) for solving unconstrained nonsmooth convex problems, firstly presented in [9] and further studied in [10], with a certain DSG method.…”

Section: Introductionmentioning

confidence: 99%

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

Freire

Lemonge

Fonseca

et al. 2018

Mathematical Problems in Engineering

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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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“…In consideration of constrained optimization problem, the hybrid intelligent algorithm is developed: this new algorithm is combined and extended on the basis of Genetic Algorithm [12][13][14][15][16][17][18][19][20][21][22][23] and Zoutendijk Algorithm. [24][25][26][27] The characteristic is as follows: both the searching definiteness and randomness are taken into account. The multipoint searching and singlepoint searching are simultaneously carried through.…”

Section: Introductionmentioning

confidence: 99%

“…The essential step of dynamical optimization model is to design a new algorithm. In consideration of constrained optimization problem, the hybrid intelligent algorithm is developed: this new algorithm is combined and extended on the basis of Genetic Algorithm and Zoutendijk Algorithm . The characteristic is as follows: both the searching definiteness and randomness are taken into account.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Optimization Model of Flatness Target Curve Based on Hybrid Intelligent Algorithm

Yan

Zhang

2016

steel research int.

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By the intelligent strategy of dynamic optimization in flatness target curve, the potential of the flatness control system can be completely fulfilled and the satisfying strip flatness can be speedily obtained. The traditional intervention pattern is static, open‐loop, non‐intelligent. In this paper, a new dynamic adjustment model of flatness target curve has been designed, by which the initial setpoint can be real‐timely regulated. The closed‐loop control system, equipped with the function of intelligent optimization and dynamic regulation, has been developed. A hybrid intelligent algorithm called ZOGE, in which both the searching definiteness and randomness are taken into account and the multipoint searching and single‐point searching are simultaneously carried through, has been proposed. The equivalent factor of flatness target curve has been optimized by function module HYBALO, which is developed on the basis of the hybrid intelligent algorithm and is operated on CFC configuration language in SIMATIC TDC controller. The testing in the field has been conducted through a 1450 mm 5‐stand tandem cold mill. The preliminary finding from the main results of testing in the field is reported: by means of the intelligent compensation model of flatness target curve, the content flatness quality of strip with thin thickness in slow rolling speed is effectively guaranteed. The maximum compensation efficiency of speed is 72.19%. The maximum compensation efficiency of thickness is 98.37%. The ability of eliminating strip flatness defect in dynamic regulation mode of flatness target curve is more powerful than the ability of eliminating strip flatness defect in conventional regulation mode.

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A feasible directions method for nonsmooth convex optimization

Cited by 10 publications

References 26 publications

A Note on Formulations of Robust Compliance Optimization Under Uncertain Loads

A Note on Formulations of Robust Compliance Optimization Under Uncertain Loads

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

Dynamic Optimization Model of Flatness Target Curve Based on Hybrid Intelligent Algorithm

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