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A new non-interior continuation method for P 0 -NCP based on a SSPM-function

Liang Fang (2011)

Applications of Mathematics

In this paper, we consider a new non-interior continuation method for the solution of nonlinear complementarity problem with P 0 -function ( P 0 -NCP). The proposed algorithm is based on a smoothing symmetric perturbed minimum function (SSPM-function), and one only needs to solve one system of linear equations and to perform only one Armijo-type line search at each iteration. The method is proved to possess global and local convergence under weaker conditions. Preliminary numerical results indicate that...

A new nonmonotone adaptive trust region algorithm

Ahmad Kamandi, Keyvan Amini (2022)

Applications of Mathematics

We propose a new and efficient nonmonotone adaptive trust region algorithm to solve unconstrained optimization problems. This algorithm incorporates two novelties: it benefits from a radius dependent shrinkage parameter for adjusting the trust region radius that avoids undesirable directions and exploits a new strategy to prevent sudden increments of objective function values in nonmonotone trust region techniques. Global convergence of this algorithm is investigated under some mild conditions....

A new one-step smoothing newton method for second-order cone programming

Jingyong Tang, Guoping He, Li Dong, Liang Fang (2012)

Applications of Mathematics

In this paper, we present a new one-step smoothing Newton method for solving the second-order cone programming (SOCP). Based on a new smoothing function of the well-known Fischer-Burmeister function, the SOCP is approximated by a family of parameterized smooth equations. Our algorithm solves only one system of linear equations and performs only one Armijo-type line search at each iteration. It can start from an arbitrary initial point and does not require the iterative points to be in the sets...

A new optimized iterative method for solving M -matrix linear systems

Alireza Fakharzadeh Jahromi, Nafiseh Nasseri Shams (2022)

Applications of Mathematics

In this paper, we present a new iterative method for solving a linear system, whose coefficient matrix is an M -matrix. This method includes four parameters that are obtained by the accelerated overrelaxation (AOR) splitting and using the Taylor approximation. First, under some standard assumptions, we establish the convergence properties of the new method. Then, by minimizing the Frobenius norm of the iteration matrix, we find the optimal parameters. Meanwhile, numerical results on test examples...

A new parameterized logarithmic kernel function for linear optimization with a double barrier term yielding the best known iteration bound

Benhadid Ayache, Saoudi Khaled (2020)

Communications in Mathematics

In this paper, we propose a large-update primal-dual interior point algorithm for linear optimization. The method is based on a new class of kernel functions which differs from the existing kernel functions in which it has a double barrier term. The investigation according to it yields the best known iteration bound O ( n log ( n ) log ( n ε ) ) for large-update algorithm with the special choice of its parameter m and thus improves the iteration bound obtained in Bai et al. [El Ghami2004] for large-update algorithm.

A new regular multiplier embedding

Gemayqzel Bouza Allende, Jürgen Guddat (2013)

Kybernetika

Embedding approaches can be used for solving non linear programs P. The idea is to define a one-parametric problem such that for some value of the parameter the corresponding problem is equivalent to P. A particular case is the multipliers embedding, where the solutions of the corresponding parametric problem can be interpreted as the points computed by the multipliers method on P. However, in the known cases, either path-following methods can not be applied or the necessary conditions for its convergence...

A new relaxation in conic form for the euclidean Steiner problem in ℜ n

Marcia Fampa, Nelson Maculan (2001)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper, we present a new mathematical programming formulation for the euclidean Steiner Tree Problem (ESTP) in ℜ n . We relax the integrality constrains on this formulation and transform the resulting relaxation, which is convex, but not everywhere differentiable, into a standard convex programming problem in conic form. We consider then an efficient computation of an ϵ -optimal solution for this latter problem using interior-point algorithm.

A New Relaxation in Conic Form for the Euclidean Steiner Problem in ℜ

Marcia Fampa, Nelson Maculan (2010)

RAIRO - Operations Research

In this paper, we present a new mathematical programming formulation for the Euclidean Steiner Tree Problem (ESTP) in ℜ. We relax the integrality constrains on this formulation and transform the resulting relaxation, which is convex, but not everywhere differentiable, into a standard convex programming problem in conic form. We consider then an efficient computation of an ϵ-optimal solution for this latter problem using interior-point algorithm.

A new series of conjectures and open questions in optimization and matrix analysis

Jean-Baptiste Hiriart-Urruty (2009)

ESAIM: Control, Optimisation and Calculus of Variations

We present below a new series of conjectures and open problems in the fields of (global) Optimization and Matrix analysis, in the same spirit as our recently published paper [J.-B. Hiriart-Urruty, Potpourri of conjectures and open questions in Nonlinear analysis and Optimization. SIAM Review 49 (2007) 255–273]. With each problem come a succinct presentation, a list of specific references, and a view on the state of the art of the subject.

A new series of conjectures and open questions in optimization and matrix analysis

Jean-Baptiste Hiriart-Urruty (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We present below a new series of conjectures and open problems in the fields of (global) Optimization and Matrix analysis, in the same spirit as our recently published paper [J.-B. Hiriart-Urruty, Potpourri of conjectures and open questions in Nonlinear analysis and Optimization. SIAM Review49 (2007) 255–273]. With each problem come a succinct presentation, a list of specific references, and a view on the state of the art of the subject.

A new simultaneous subgradient projection algorithm for solving a multiple-sets split feasibility problem

Yazheng Dang, Yan Gao (2014)

Applications of Mathematics

In this paper, we present a simultaneous subgradient algorithm for solving the multiple-sets split feasibility problem. The algorithm employs two extrapolated factors in each iteration, which not only improves feasibility by eliminating the need to compute the Lipschitz constant, but also enhances flexibility due to applying variable step size. The convergence of the algorithm is proved under suitable conditions. Numerical results illustrate that the new algorithm has better convergence than the...

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