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Optimization Methods and Software Volume 25, 2010 - Issue 6: The International Conference on Engineering Optimization (EngOpt 2008)
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The International Conference on Engineering Optimization (EngOpt 2008)

Interior proximal algorithm with variable metric for second-order cone programming: applications to structural optimization and support vector machines

Felipe Alvarez Departamento de Ingeniería Matemática, Centro de Modelamiento Matemático (CNRS UMI 2807), FCFM, Universidad de Chile, Blanco Encalada 2120, Santiago, Chile
,
Julio López Departamento de Ingeniería Matemática, Centro de Modelamiento Matemático (CNRS UMI 2807), FCFM, Universidad de Chile, Blanco Encalada 2120, Santiago, ChileCorrespondence[email protected]
&
C. Héctor Ramírez Departamento de Ingeniería Matemática, Centro de Modelamiento Matemático (CNRS UMI 2807), FCFM, Universidad de Chile, Blanco Encalada 2120, Santiago, Chile
Pages 859-881 | Received 30 Oct 2008, Accepted 05 Nov 2009, Published online: 04 Mar 2010

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Alfredo Canelas, Miguel Carrasco & Julio López. (2019) A feasible direction algorithm for nonlinear second-order cone programs. Optimization Methods and Software 34:6, pages 1322-1341.
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Julio López & Erik Alex Papa Quiroz. (2017) Construction of proximal distances over symmetric cones. Optimization 66:8, pages 1301-1321.
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Felipe Alvarez & Julio López. (2016) Interior proximal bundle algorithm with variable metric for nonsmooth convex symmetric cone programming. Optimization 65:9, pages 1757-1779.
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Articles from other publishers (29)

Zemin Zong & Xuewen Mu. (2023) A new formulation for second-order cone programming support vector machine. International Journal of Machine Learning and Cybernetics.
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Roberto Andreani, Gabriel Haeser, Leonardo M. Mito, C. Héctor Ramírez & Thiago P. Silveira. (2022) Global Convergence of Algorithms Under Constant Rank Conditions for Nonlinear Second-Order Cone Programming. Journal of Optimization Theory and Applications 195:1, pages 42-78.
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Sebastián Maldonado, Julio López & Miguel Carrasco. (2022) The Cobb-Douglas Learning Machine. Pattern Recognition 128, pages 108701.
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Yaling Zhang & Hongwei Liu. (2022) A Barzilai and Borwein regularization feasible direction algorithm for convex nonlinear SOC programming with linear constraints. Journal of Computational and Applied Mathematics 401, pages 113781.
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Jun Ma & Guolin Yu. (2022) Regularized twin minimax probability machine for pattern classification and regression. Engineering Applications of Artificial Intelligence 107, pages 104550.
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Qi Zhao & Zhongwen Chen. (2020) A Line Search Penalty-Free Method for Nonlinear Second-Order Cone Programming. Acta Applicandae Mathematicae 170:1, pages 291-317.
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Jun Ma & Jumei Shen. (2020) RETRACTED: A novel twin minimax probability machine for classification and regression. Knowledge-Based Systems 196, pages 105703.
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Alexander J. ZaslavskiAlexander J. Zaslavski. 2020. Convex Optimization with Computational Errors. Convex Optimization with Computational Errors 243 258 .
Julio López, Sebastián Maldonado & Miguel Carrasco. (2019) Robust nonparallel support vector machines via second-order cone programming. Neurocomputing 364, pages 227-238.
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Sebastián Maldonado, Miguel Carrasco & Julio López. (2019) Regularized minimax probability machine. Knowledge-Based Systems 177, pages 127-135.
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Julio López & Sebastián Maldonado. (2018) Robust twin support vector regression via second-order cone programming. Knowledge-Based Systems 152, pages 83-93.
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Julio López, Sebastián Maldonado & Miguel Carrasco. (2018) Double regularization methods for robust feature selection and SVM classification via DC programming. Information Sciences 429, pages 377-389.
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Sebastián Maldonado & Julio López. (2017) Robust kernel-based multiclass support vector machines via second-order cone programming. Applied Intelligence 46:4, pages 983-992.
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Sebastián Maldonado, Julio López & Miguel Carrasco. (2016) A second-order cone programming formulation for twin support vector machines. Applied Intelligence 45:2, pages 265-276.
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Miguel Carrasco, Julio López & Sebastián Maldonado. (2016) A second-order cone programming formulation for nonparallel hyperplane support vector machine. Expert Systems with Applications 54, pages 95-104.
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Julio López, Sebastián Maldonado & Miguel Carrasco. (2015) A novel multi-class SVM model using second-order cone constraints. Applied Intelligence 44:2, pages 457-469.
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Julio López & Sebastián Maldonado. (2016) Multi-class second-order cone programming support vector machines. Information Sciences 330, pages 328-341.
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Alexander J. ZaslavskiAlexander J. Zaslavski. 2016. Numerical Optimization with Computational Errors. Numerical Optimization with Computational Errors 149 168 .
E.A. Papa Quiroz, L. Mallma Ramirez & P.R. Oliveira. (2015) An inexact proximal method for quasiconvex minimization. European Journal of Operational Research 246:3, pages 721-729.
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Pierre Frankel, Guillaume Garrigos & Juan Peypouquet. (2014) Splitting Methods with Variable Metric for Kurdyka??ojasiewicz Functions and General Convergence Rates. Journal of Optimization Theory and Applications 165:3, pages 874-900.
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Boris S. Mordukhovich, Ji?? V. Outrata & H?ctor Ram?rez C.. (2015) Second-Order Variational Analysis in Conic Programming with Applications to Optimality and Stability. SIAM Journal on Optimization 25:1, pages 76-101.
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Sebastián Maldonado & Julio López. (2014) Alternative second-order cone programming formulations for support vector classification. Information Sciences 268, pages 328-341.
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Sebastián Maldonado & Julio López. (2014) Imbalanced data classification using second-order cone programming support vector machines. Pattern Recognition 47:5, pages 2070-2079.
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Julio L?pez, R?ben L?pez & H?ctor C. Ram?rez. (2012) Linear Complementarity Problems over Symmetric Cones: Characterization of Q b -transformations and Existence Results. Journal of Optimization Theory and Applications 159:3, pages 741-768.
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Paul Bosch, Julio L?pez, H?ctor Ram?rez & Hugo Robotham. (2013) Support vector machine under uncertainty: An application for hydroacoustic classification of fish-schools in Chile. Expert Systems with Applications 40:10, pages 4029-4034.
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Emilio Carrizosa & Dolores Romero Morales. (2013) Supervised classification and mathematical optimization. Computers & Operations Research 40:1, pages 150-165.
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Adelaide Cerveira, Agostinho Agra, Fernando Bastos & Joaquim Gromicho. (2012) A new Branch and Bound method for a discrete truss topology design problem. Computational Optimization and Applications 54:1, pages 163-187.
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Alexander J. Zaslavski. (2011) Inexact Proximal Point Methods in Metric Spaces. Set-Valued and Variational Analysis 19:4, pages 589-608.
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Jiří V. Outrata & Héctor Ramírez C.. (2011) On the Aubin Property of Critical Points to Perturbed Second-Order Cone Programs. SIAM Journal on Optimization 21:3, pages 798-823.
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