Addressing the greediness phenomenon in Nonlinear Programming by means of Proximal Augmented Lagrangians

Castelani, Emerson Vitor; Martinez, André Luís Machado; Martínez, José Mário; Svaiter, B. F.

doi:10.1007/s10589-009-9271-4

Cited by 8 publications

(5 citation statements)

References 9 publications

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“…6 and 7a evidences that non-linear programming methods in the first iterations may preferentially seek better values of the objective function over feasibility. This behaviour is described in the literature as the voracity in reducing the objective function magnitude, which has already been reported in [36] for the ALM method, but considering the dimension of the networks treated in scenario A and such characteristic did not affect the convergence of the method herein. However, we can highlight that ALM demanded a greater number of iterations to achieve convergence when compared to the SQP method.…”

Section: Power Assignment Optimisation (Scenario A)supporting

confidence: 61%

Hopfield learning‐based and non‐linear programming methods for resource allocation in OCDMA networks

et al. 2020

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This paper proposes the deployment of the Hopfield's artificial neural network (H-NN) approach to optimally assign power in optical code division multiple access (OCDMA) systems. Figures of merit such as feasibility of solutions and complexity are compared with the classical power allocation methods found in the literature, such as Sequential Quadratic Programming (SQP) and Augmented Lagrangian Method (ALM). The analyzed methods are used to solve constrained nonlinear optimization problems in the context of resource allocation for optical networks, specially to deal with the energy efficiency (EE) in OCDMA networks. The promising performance-complexity tradeoff of the modified H-NN is demonstrated through numerical results performed in comparison with classic methods for general problems in nonlinear programming. The evaluation is carried out considering challenging OCDMA networks in which different levels of QoS were considered for large numbers of optical users.

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Section: Power Assignment Optimisation (Scenario A)supporting

confidence: 61%

Hopfield learning‐based and non‐linear programming methods for resource allocation in OCDMA networks

et al. 2020

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“…But, by the inertia correction procedure, the identity (12), and the Sylvester Law of Inertia, we have that…”

Section: If a Limit Point Of {Xmentioning

confidence: 99%

“…The considered set of 283 problems from the CUTEst collection includes 45 problems (representing 16% of the problems) that are quadratic programming reformulations of linear complementarity problems (provided by Michael Ferris). In 11 out of this 45 problems, SECO presented a phenomenon named greediness in [12,10] that may affect penalty and Lagrangian methods when the objective function takes very low values (perhaps going to −∞) in the non-feasible region. In this case, iterates of the subproblems' solver may be attracted by undesired minimizers, especially at the first outer iterations, and overall convergence may fail to occur.…”

Section: Problems With Equality Constraints and Bound Constraintsmentioning

confidence: 99%

Sequential equality-constrained optimization for nonlinear programming

2016

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A novel idea is proposed for solving optimization problems with equality constraints and bounds on the variables. In the spirit of Sequential Quadratic Programming and Sequential Linearly-Constrained Programming, the new proposed approach approximately solves, at each iteration, an equality-constrained optimization problem. The bound constraints are handled in outer iterations by means of an Augmented Lagrangian scheme. Global convergence of the method follows from well-established nonlinear programming theories. Numerical experiments are presented.

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“…In greedy cases, the step restriction avoids jumps in the direction of unconstrained undesired minimizers. The trust-region restriction is more effective than the proximal strategy of [1] because it tends to definitely exclude the unconstrained minimum from the domain.…”

Section: Algorithmmentioning

confidence: 99%

Outer Trust-Region Method for Constrained Optimization

Birgin

Castelani

Martinez

et al. 2011

J Optim Theory Appl

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Given an algorithm A for solving some mathematical problem based on the iterative solution of simpler subproblems, an Outer Trust-Region (OTR) modification of A is the result of adding a trust-region constraint to each subproblem. The trust-region size is adaptively updated according to the behavior of crucial variables. The new subproblems should not be more complex than the original ones and the convergence properties of the OTR algorithm should be the same as those of Algorithm A. In the present work, the OTR approach is exploited in connection with the "greediness phenomenon" of Nonlinear Programming. Convergence results for an OTR version of an Augmented Lagrangian method for nonconvex constrained optimization are proved and numerical experiments are presented.

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Addressing the greediness phenomenon in Nonlinear Programming by means of Proximal Augmented Lagrangians

Abstract: Nonlinear programming, Greediness, Augmented Lagrangian method, Regularization,

Cited by 8 publications

References 9 publications

Hopfield learning‐based and non‐linear programming methods for resource allocation in OCDMA networks

Hopfield learning‐based and non‐linear programming methods for resource allocation in OCDMA networks

Sequential equality-constrained optimization for nonlinear programming

Outer Trust-Region Method for Constrained Optimization

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