Trust-region quadratic methods for nonlinear systems of mixed equalities and inequalities

Macconi, M.; Morini, Benedetta; Porcelli, Margherita

doi:10.1016/j.apnum.2008.03.028

Cited by 41 publications

(36 citation statements)

References 29 publications

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“…In this paper we present a new Matlab solver which implements an iterative procedure for problem (1) and handles systems (2) of nonlinear equalities and inequalities. Our proposal is based on the results presented by the authors in the recent papers [13,14]. In particular, in [13] a trust-region Gauss-Newton method and a trust-region Levenberg-Marquardt method for solving (1) are presented.…”

Section: Introductionmentioning

confidence: 99%

“…Our proposal is based on the results presented by the authors in the recent papers [13,14]. In particular, in [13] a trust-region Gauss-Newton method and a trust-region Levenberg-Marquardt method for solving (1) are presented. These methods can solve overdetermined and underdetermined least-squares problems, generate feasible iterates and rely on matrix factorizations.…”

Section: Introductionmentioning

confidence: 99%

“…If a solution to the nonlinear system cannot be found, a local minimizer for the violations of the equations is computed. Problem (1) is also a suitable reformulation of systems of nonlinear equalities and inequalities [13] which arise in model formulation design, parameter identification problems, detection of feasible points in nonlinear programming and take the form…”

Section: Introductionmentioning

confidence: 99%

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TRESNEI, a Matlab trust-region solver for systems of nonlinear equalities and inequalities

Morini

Porcelli

2010

Comput Optim Appl

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The Matlab implementation of a trust-region Gauss-Newton method for bound-constrained nonlinear least-squares problems is presented. The solver, called TRESNEI, is adequate for zero and small-residual problems and handles the solution of nonlinear systems of equalities and inequalities. The structure and the usage of the solver are described and an extensive numerical comparison with functions from the Matlab Optimization Toolbox is carried out.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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TRESNEI, a Matlab trust-region solver for systems of nonlinear equalities and inequalities

Morini

Porcelli

2010

Comput Optim Appl

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“…In this case, the system of inequalities has been studied extensively because of its various applications in data analysis, set separation problems, computer-aided design problems, image reconstructions, and detection on the feasibility of nonlinear programming. Already many iteration methods exist for solving such inequalities; see, for example [5][6][7][8][9]. It is well known that the positive semi-definite matrix cone, the second-order cone, and the nonnegative orthant cone n + as common symmetric cones have many applications in practice and are studied mostly.…”

Section: Introductionmentioning

confidence: 99%

A smoothing-type algorithm for solving inequalities under the order induced by a symmetric cone

Zhang

2011

J Inequal Appl

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In this article, we consider the numerical method for solving the system of inequalities under the order induced by a symmetric cone with the function involved being monotone. Based on a perturbed smoothing function, the underlying system of inequalities is reformulated as a system of smooth equations, and a smoothing-type method is proposed to solve it iteratively so that a solution of the system of inequalities is found. By means of the theory of Euclidean Jordan algebras, the algorithm is proved to be well defined, and to be globally convergent under weak assumptions and locally quadratically convergent under suitable assumptions. Preliminary numerical results indicate that the algorithm is effective.

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“…If n = m and I = ∅, the system (SNEI) reduces into a system of nonlinear equations, one classical problem in mathematics, for which there are many wellknown methods, such as Newton-type methods, secant methods, and trust-region methods (see [3,4,5,11] etc.). Similarly, in recent years these methods are also proposed to solve the system (SNEI) (see [6,7,15,16,17,18,19,22,26] …”

Section: Introductionmentioning

confidence: 99%

A filled function method for nonlinear systems of equalities and inequalities

Wan

Yuan

Chen

2012

Comput. Appl. Math.

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Abstract. In this paper a filled function method is suggested for solving nonlinear systems of equalities and inequalities. Firstly, the original problem is reformulated into an equivalent constrained global optimization problem. Subsequently, a new filled function with one parameter is constructed based on the special characteristics of the reformulated optimization problem.Some properties of the filled function are studied and discussed. Finally, an algorithm based on the proposed filled function for solving nonlinear systems of equalities and inequalities is presented. The objective function value can be reduced by half in each iteration of our filled function algorithm. The implementation of the algorithm on several test problems is reported with numerical results. 65K05, 90C30. Mathematical subject classification:

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Trust-region quadratic methods for nonlinear systems of mixed equalities and inequalities

Cited by 41 publications

References 29 publications

TRESNEI, a Matlab trust-region solver for systems of nonlinear equalities and inequalities

TRESNEI, a Matlab trust-region solver for systems of nonlinear equalities and inequalities

A smoothing-type algorithm for solving inequalities under the order induced by a symmetric cone

A filled function method for nonlinear systems of equalities and inequalities

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