Solving the Perceptron Problem by deterministic optimization approach based on DC programming and DCA

被引：1

作者：

An, Le Thi Hoai ^{[1
]}

Minh, Le Hoai ^{[1
]}

Tao, Pham Dinh ^{[2
]}

Bouvry, Pascal ^{[3
]}

机构：

[1] Univ Paul Verlaine Metz, UFR MIM, Lab Theoret & Appl Comp Sci, F-57045 Metz, France

[2] Natl Inst Appl Sci Rouen, Lab Modelling Optmizat & Operat Res, F-76131 Mont St Aignan, France

[3] Univ Luxemourg, Comp Sci Res Unit, L-1359 Luxembourg, Luxembourg

来源：

2009 7TH IEEE INTERNATIONAL CONFERENCE ON INDUSTRIAL INFORMATICS, VOLS 1 AND 2 | 2009年

关键词：

Cryptanalysis; Identification scheme; Perceptron Problem; DC programming; DCA; IDENTIFICATION;

D O I：

10.1109/INDIN.2009.5195807

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

The Perceptron Problem (PP) appeared for the first time in the Learning Machines and is very useful for zero-knowledge identification schemes in cryptology. The problem is NP-complete and no deterministic algorithm is known to date. In this paper we develop a deterministic method based on DC (Difference of Convex functions) programming and DCA (DC optimization Algorithms), an innovative approach in nonconvex programming framework. We first formulate the PP as a concave minimization programming problem. Then, we show how to apply DC programming and DCA for the resulting problem. Numerical results demonstrate that the proposed algorithm is promising: its is very fast and can efficiently solve the Perceptron Problem with large sizes.

引用

页码：222 / +

页数：2

共 50 条

[41] A deterministic optimization approach for the unit commitment problem
Marcovecchio, Marian G.
Novais, Augusto Q.
Grossmann, Ignacio E.
21ST EUROPEAN SYMPOSIUM ON COMPUTER AIDED PROCESS ENGINEERING, 2011, 29 : 532 - 536
[42] Simulation Optimization Approach for Solving Stochastic Programming
Akl, Amany M.
Sarker, Ruhul A.
Essam, Daryl L.
2017 2ND IEEE INTERNATIONAL CONFERENCE ON COMPUTATIONAL INTELLIGENCE AND APPLICATIONS (ICCIA), 2017, : 161 - 165
[43] DC Programming and DCA for Solving Minimum Sum-of-Squares Clustering Using Weighted Dissimilarity Measures
Le Hoai Minh
Ta Minh Thuy
TRANSACTIONS ON COMPUTATIONAL COLLECTIVE INTELLIGENCE XIII, 2014, 8342 : 113 - 131
[44] The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems
An, LTH
Tao, PD
ANNALS OF OPERATIONS RESEARCH, 2005, 133 (1-4) : 23 - 46
[45] The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems
Le Thi Hoai An
Pham Dinh Tao
Annals of Operations Research, 2005, 133 : 23 - 46
[46] A global optimization algorithm for solving linear programming problem
Cavalcante, JRR
de Souza, FMC
MANAGEMENT AND CONTROL OF PRODUCTION AND LOGISTICS, VOL 1 AND 2, 1998, : 513 - 515
[47] Noisy image segmentation by a robust clustering algorithm based on DC programming and DCA
An, Le Thi Hoai
Minh, Le Hoai
Phuc, Nguyen Trong
Tao, Pham Dinh
ADVANCES IN DATA MINING, PROCEEDINGS: MEDICAL APPLICATIONS, E-COMMERCE, MARKETING, AND THEORETICAL ASPECTS, 2008, 5077 : 72 - +
[48] An Approach to Fractional Programming via DC Optimization
Gruzdeva, Tatiana
Strekalovskiy, Alexander
NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS (NUMTA-2016), 2016, 1776
[49] A Generalized Equilibrium Value-based Approach for Solving Fuzzy Programming Problem
Jin, Chenxia
Shi, Yan
Yang, Meng
Li, Fachao
2014 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE), 2014, : 1219 - 1225
[50] A goal programming approach for solving the random interval linear programming problem
Arjmandzadeh, Ziba
Safi, Mohammadreza
TURKISH JOURNAL OF MATHEMATICS, 2017, 41 (04) : 775 - 786

← 1 2 3 4 5 →