22 Result(s)
within
E. G. Birgin
Optimization
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Article
Safeguarded augmented Lagrangian algorithms with scaled stop** criterion for the subproblems
At each iteration of the safeguarded augmented Lagrangian algorithm Algencan, a bound-constrained subproblem consisting of the minimization of the Powell–Hestenes–Rockafellar augmented Lagrangian function is c...
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Article
Relax-and-Fix Heuristics Applied to a Real-World Lot Sizing and Scheduling Problem in the Personal Care Consumer Goods Industry
This paper addresses an integrated lot sizing and scheduling problem in the industry of consumer goods for personal care, a very competitive market in which good customer service and cost management are crucia...
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Article
On complexity and convergence of high-order coordinate descent algorithms for smooth nonconvex box-constrained minimization
Coordinate descent methods have considerable impact in global optimization because global (or, at least, almost global) minimization is affordable for low-dimensional problems. Coordinate descent methods with ...
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Block coordinate descent for smooth nonconvex constrained minimization
At each iteration of a block coordinate descent method one minimizes an approximation of the objective function with respect to a generally small set of variables subject to constraints in which these variable...
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Article
Accelerated derivative-free nonlinear least-squares applied to the estimation of Manning coefficients
A general framework for solving nonlinear least squares problems without the employment of derivatives is proposed in the present paper together with a new general global convergence theory. With the aim to co...
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Article
On the solution of linearly constrained optimization problems by means of barrier algorithms
Many practical problems require the solution of large-scale constrained optimization problems for which preserving feasibility is a key issue, and the evaluation of the objective function is very expensive. In...
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On the use of third-order models with fourth-order regularization for unconstrained optimization
In a recent paper (Birgin et al. in Math Program 163(1):359–368, 2017), it was shown that, for the smooth unconstrained optimization problem, worst-case evaluation complexity \(O(\epsilon ^{-(p+1)/p})\)O(ϵ-(p+1)/
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Article
A Newton-like method with mixed factorizations and cubic regularization for unconstrained minimization
A Newton-like method for unconstrained minimization is introduced in the present work. While the computer work per iteration of the best-known implementations may need several factorizations or may use rather ...
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Article
Augmented Lagrangians with constrained subproblems and convergence to second-order stationary points
Augmented Lagrangian methods with convergence to second-order stationary points in which any constraint can be penalized or carried out to the subproblems are considered in this work. The resolution of each su...
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Article
On the minimization of possibly discontinuous functions by means of pointwise approximations
A general approach for the solution of possibly discontinuous optimization problems by means of pointwise (perhaps smooth) approximations will be proposed. It will be proved that sequences generated by pointwi...
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Article
A nonlinear programming model with implicit variables for packing ellipsoids
The problem of packing ellipsoids is considered in the present work. Usually, the computational effort associated with numerical optimization methods devoted to packing ellipsoids grows quadratically with resp...
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Article
Sequential equality-constrained optimization for nonlinear programming
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 programmi...
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Article
Packing ellipsoids by nonlinear optimization
In this paper, continuous and differentiable nonlinear programming models and algorithms for packing ellipsoids in the n-dimensional space are introduced. Two different models for the non-overlap** and models f...
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Article
On the application of an Augmented Lagrangian algorithm to some portfolio problems
Algencan is a freely available piece of software that aims to solve smooth large-scale constrained optimization problems. When applied to specific problems, obtaining a good performance in terms of efficacy an...
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Article
Optimality properties of an Augmented Lagrangian method on infeasible problems
Sometimes, the feasible set of an optimization problem that one aims to solve using a Nonlinear Programming algorithm is empty. In this case, two characteristics of the algorithm are desirable. On the one hand...
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Article
Augmented Lagrangians with possible infeasibility and finite termination for global nonlinear programming
In a recent paper, Birgin, Floudas and Martínez introduced an augmented Lagrangian method for global optimization. In their approach, augmented Lagrangian subproblems are solved using the
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Article
Symmetry-breaking constraints for packing identical rectangles within polyhedra
Two problems related to packing identical rectangles within a polyhedron are tackled in the present work. Rectangles are allowed to differ only by horizontal or vertical translations and possibly 90° rotations...
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Article
Low order-value approach for solving VaR-constrained optimization problems
In Low Order-Value Optimization (LOVO) problems the sum of the r smallest values of a finite sequence of q functions is involved as the objective to be minimized or as a constraint. The latter case is considered ...
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Article
Second-order negative-curvature methods for box-constrained and general constrained optimization
A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a c...
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Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization
Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained ...
