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Published in: Neural Processing Letters 2/2022

03-01-2022

A One-Layer Recurrent Neural Network for Interval-Valued Optimization Problem with Linear Constraints

Authors: Yueqiu Li, Chunna Zeng, Bing Li, Jin Hu

Published in: Neural Processing Letters | Issue 2/2022

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Abstract

In this paper, the interval-valued optimization problem is converted to a general problem in the parametric form and its solution is efficient. We present a one-layer recurrent neural network for solving this interval-valued optimization problem with linear constraints. Based on this approach, we prove that the recurrent neural network is stable in the sense of Lyapunov and the equilibrium point of the neural network is globally convergent to the optimal solution. The proposed approach improves the algorithm for the interval-valued optimization and the model is easy to implement. Finally, two numerical examples are provided to show the feasibility and effectiveness of the proposed approach.

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Literature
1.
2.
go back to reference Thuente DJ (1980) Duality theory for generalized linear programs with computational methods. Oper Res 28(4):1005–1011MathSciNetCrossRef Thuente DJ (1980) Duality theory for generalized linear programs with computational methods. Oper Res 28(4):1005–1011MathSciNetCrossRef
3.
go back to reference Wu HC (2011) Interval-valued optimization problems based on different solution concepts. Pac J Optim 7(1):173–193MathSciNetMATH Wu HC (2011) Interval-valued optimization problems based on different solution concepts. Pac J Optim 7(1):173–193MathSciNetMATH
4.
go back to reference Ghosh D (2017) Newton method to obtain efficient solutions of the optimization problems with interval-valued objective functions. J Appl Math Comput Ghosh D (2017) Newton method to obtain efficient solutions of the optimization problems with interval-valued objective functions. J Appl Math Comput
5.
go back to reference Su ZG, Wang PH (2015) Parameter estimation from interval-valued data using the expectation-maximization algorithm. J Stat Comput Simul 85(1–3):320–338MathSciNetCrossRef Su ZG, Wang PH (2015) Parameter estimation from interval-valued data using the expectation-maximization algorithm. J Stat Comput Simul 85(1–3):320–338MathSciNetCrossRef
6.
go back to reference Wu HC (2007) The Karush–Kuhn–Tucker optimality conditions in an optimization problem with interval-valued objective function. Eur J Oper Res 176(1):46–59MathSciNetCrossRef Wu HC (2007) The Karush–Kuhn–Tucker optimality conditions in an optimization problem with interval-valued objective function. Eur J Oper Res 176(1):46–59MathSciNetCrossRef
7.
go back to reference Chen S (2020) The KKT optimality conditions for optimization problem with interval-valued objective function on Hadamard manifolds. Optimization 1:1–20 Chen S (2020) The KKT optimality conditions for optimization problem with interval-valued objective function on Hadamard manifolds. Optimization 1:1–20
8.
go back to reference Bhurjee AK, Panda G (2012) Efficient solution of interval optimization problem. Math Methods Oper Res 76(3):273–288MathSciNetCrossRef Bhurjee AK, Panda G (2012) Efficient solution of interval optimization problem. Math Methods Oper Res 76(3):273–288MathSciNetCrossRef
9.
go back to reference Chalco-Cano Y (2015) A note on optimality conditions to interval optimization problems. In: 2015 conference of the international fuzzy systems association and the European society for fuzzy logic and technology (IFSA-EUSFLAT-15) Chalco-Cano Y (2015) A note on optimality conditions to interval optimization problems. In: 2015 conference of the international fuzzy systems association and the European society for fuzzy logic and technology (IFSA-EUSFLAT-15)
10.
go back to reference Sun J, Miao Z, Gong D (2019) Interval multiobjective optimization with memetic algorithms. IEEE Trans Cybern 48(99):1–14CrossRef Sun J, Miao Z, Gong D (2019) Interval multiobjective optimization with memetic algorithms. IEEE Trans Cybern 48(99):1–14CrossRef
11.
go back to reference Wang L, Chen Z, Yang G (2020) An interval uncertain optimization method using back-propagation neural network differentiation. Comput Methods Appl Mech Eng 366 Wang L, Chen Z, Yang G (2020) An interval uncertain optimization method using back-propagation neural network differentiation. Comput Methods Appl Mech Eng 366
12.
go back to reference Tao Q, Xin L, Cui X (2005) A linear optimization neural network for associative memory. Appl Math Comput 171(2):1119–1128MathSciNetMATH Tao Q, Xin L, Cui X (2005) A linear optimization neural network for associative memory. Appl Math Comput 171(2):1119–1128MathSciNetMATH
13.
go back to reference Guo Z, Baruah SK (2016) A neurodynamic approach for real-time scheduling via maximizing piecewise linear utility. IEEE Trans Neural Netw Learn Syst 27(2):238–248MathSciNetCrossRef Guo Z, Baruah SK (2016) A neurodynamic approach for real-time scheduling via maximizing piecewise linear utility. IEEE Trans Neural Netw Learn Syst 27(2):238–248MathSciNetCrossRef
14.
go back to reference Yang Y, Guo Z, Xiong H, Ding DW (2019) Data-driven robust control of discrete-time uncertain linear systems via off-policy reinforcement learning. IEEE Trans Neural Netw Learn Syst 30(12):3735–3747MathSciNetCrossRef Yang Y, Guo Z, Xiong H, Ding DW (2019) Data-driven robust control of discrete-time uncertain linear systems via off-policy reinforcement learning. IEEE Trans Neural Netw Learn Syst 30(12):3735–3747MathSciNetCrossRef
15.
go back to reference Hu X, Wang J (2007) Design of general projection neural networks for solving monotone linear variational inequalities and linear and quadratic optimization problems. IEEE Trans Syst Man Cybern Part B Cybern A Publ IEEE Syst Man Cybern Soc 37(5):1414–1421CrossRef Hu X, Wang J (2007) Design of general projection neural networks for solving monotone linear variational inequalities and linear and quadratic optimization problems. IEEE Trans Syst Man Cybern Part B Cybern A Publ IEEE Syst Man Cybern Soc 37(5):1414–1421CrossRef
16.
go back to reference Tank DW, Hopfield JJ (1986) Simple neural optimization networks: an A/D converter, signal decision circuit, and a linear programming circuit. IEEE Trans Circuits Syst 33(5):533–541CrossRef Tank DW, Hopfield JJ (1986) Simple neural optimization networks: an A/D converter, signal decision circuit, and a linear programming circuit. IEEE Trans Circuits Syst 33(5):533–541CrossRef
17.
18.
go back to reference Xia Y, Wang J (2005) A recurrent neural network for solving nonlinear convex programs subject to linear constraints. IEEE Trans Neural Netw 16(2):379–386CrossRef Xia Y, Wang J (2005) A recurrent neural network for solving nonlinear convex programs subject to linear constraints. IEEE Trans Neural Netw 16(2):379–386CrossRef
19.
go back to reference Xue X, Bian W (2008) Subgradient-based neural networks for nonsmooth convex optimization Problems. IEEE Trans Circuits Syst I Regular Pap 55(8):2378–2391MathSciNetCrossRef Xue X, Bian W (2008) Subgradient-based neural networks for nonsmooth convex optimization Problems. IEEE Trans Circuits Syst I Regular Pap 55(8):2378–2391MathSciNetCrossRef
20.
go back to reference Xue X, Bian W (2009) Subgradient-based neural networks for nonsmooth convex optimization problems. IEEE Trans Neural Netw 20(6):1024–10381CrossRef Xue X, Bian W (2009) Subgradient-based neural networks for nonsmooth convex optimization problems. IEEE Trans Neural Netw 20(6):1024–10381CrossRef
21.
go back to reference Arjmandzadeh Z, Safi (2017) A new neural network model for solving random interval linear programming problems. Neural Netw 89, 11 Arjmandzadeh Z, Safi (2017) A new neural network model for solving random interval linear programming problems. Neural Netw 89, 11
22.
go back to reference Nikseresht A, Nazemi A (2018) A novel neural network model for solving a class of nonlinear semidefinite programming problems. J Comput Appl Math 338:69–79MathSciNetCrossRef Nikseresht A, Nazemi A (2018) A novel neural network model for solving a class of nonlinear semidefinite programming problems. J Comput Appl Math 338:69–79MathSciNetCrossRef
23.
go back to reference Li W, Bian W, Xue X (2020) Projected neural network for a class of non-Lipschitz optimization problems with linear constraints. IEEE Trans Neural Netw Learn Syst 31(9):3361–3373MathSciNetCrossRef Li W, Bian W, Xue X (2020) Projected neural network for a class of non-Lipschitz optimization problems with linear constraints. IEEE Trans Neural Netw Learn Syst 31(9):3361–3373MathSciNetCrossRef
24.
go back to reference Liu, Q, Wang J (2008) A one-layer recurrent neural network for convex programming. In: IEEE International joint conference on neural networks (IEEE world congress on computational intelligence) Liu, Q, Wang J (2008) A one-layer recurrent neural network for convex programming. In: IEEE International joint conference on neural networks (IEEE world congress on computational intelligence)
25.
go back to reference Liu Q, Wang J (2011) A one-layer recurrent neural network for constrained single-ratio linear fractional programming. In: IEEE international symposium on circuits & systems Liu Q, Wang J (2011) A one-layer recurrent neural network for constrained single-ratio linear fractional programming. In: IEEE international symposium on circuits & systems
26.
go back to reference Qin S, Yang X, Xue X (2017) A one-layer recurrent neural network for pseudoconvex optimization problems with equality and inequality constraints. IEEE Trans Cybern 47(10):3063–3074CrossRef Qin S, Yang X, Xue X (2017) A one-layer recurrent neural network for pseudoconvex optimization problems with equality and inequality constraints. IEEE Trans Cybern 47(10):3063–3074CrossRef
27.
go back to reference Liu Q, Guo Z, Wang J (2012) A one-layer recurrent neural network for constrained pseudoconvex optimization and its application for dynamic portfolio optimization. Neural Netw 26:99–109CrossRef Liu Q, Guo Z, Wang J (2012) A one-layer recurrent neural network for constrained pseudoconvex optimization and its application for dynamic portfolio optimization. Neural Netw 26:99–109CrossRef
28.
go back to reference Guo Z, Liu Q, Wang J (2014) A simplified recurrent neural network for pseudoconvex optimization subject to linear equality constraints. IEEE Trans Neural Netw 19(12):789–798MathSciNet Guo Z, Liu Q, Wang J (2014) A simplified recurrent neural network for pseudoconvex optimization subject to linear equality constraints. IEEE Trans Neural Netw 19(12):789–798MathSciNet
29.
go back to reference Liu Q, Wang J (2013) A one-layer projection neural network for nonsmooth optimization subject to linear equalities and bound constraints. IEEE Trans Neural Netw Learn Syst 24(5):812–824CrossRef Liu Q, Wang J (2013) A one-layer projection neural network for nonsmooth optimization subject to linear equalities and bound constraints. IEEE Trans Neural Netw Learn Syst 24(5):812–824CrossRef
30.
go back to reference Liu Q, Dang C, Huang T (2013) A one-layer recurrent neural network for real-time portfolio optimization with probability criterion. IEEE Trans Cybern 43(1):14–23CrossRef Liu Q, Dang C, Huang T (2013) A one-layer recurrent neural network for real-time portfolio optimization with probability criterion. IEEE Trans Cybern 43(1):14–23CrossRef
31.
go back to reference Liu Q, Huang T, Wang J (2017) One-layer continuous-and discrete-time projection neural networks for solving variational inequalities and related optimization problems. IEEE Trans Neural Netw Learn Syst 25(7):1308–1318CrossRef Liu Q, Huang T, Wang J (2017) One-layer continuous-and discrete-time projection neural networks for solving variational inequalities and related optimization problems. IEEE Trans Neural Netw Learn Syst 25(7):1308–1318CrossRef
32.
go back to reference Guo Z, Wang J (2010) A neurodynamic optimization approach to constrained sparsity maximization based on alternative objective functions. In: The 2010 International joint conference on neural networks (IJCNN) Guo Z, Wang J (2010) A neurodynamic optimization approach to constrained sparsity maximization based on alternative objective functions. In: The 2010 International joint conference on neural networks (IJCNN)
33.
go back to reference Ha NT, Strodiot JJ (2018) On the global exponential stability of a projected dynamical system for strongly pseudomonotone variational inequalities. Optim Lett Ha NT, Strodiot JJ (2018) On the global exponential stability of a projected dynamical system for strongly pseudomonotone variational inequalities. Optim Lett
34.
go back to reference Bazraa MS, Sherali HD, Shetty CM (1993) Nonlinear programming theory and algorithms. John Wiley, New York Bazraa MS, Sherali HD, Shetty CM (1993) Nonlinear programming theory and algorithms. John Wiley, New York
35.
36.
go back to reference Xia Y (1996) A new neural network for solving linear and quadratic programming problems. IEEE Trans Neural Netw 7(6):1544–1548CrossRef Xia Y (1996) A new neural network for solving linear and quadratic programming problems. IEEE Trans Neural Netw 7(6):1544–1548CrossRef
37.
go back to reference Long C, Hou ZG, Min T (2007) A recurrent neural network for non-smooth nonlinear programming problems. In: International joint conference on neural networks Long C, Hou ZG, Min T (2007) A recurrent neural network for non-smooth nonlinear programming problems. In: International joint conference on neural networks
38.
go back to reference Pattananupong U, Chaiyaratana N, Tongpadungrod R (2007) Genetic programming and neural networks as interpreters for a distributive tactile sensing system. In: IEEE congress on evolutionary computation Pattananupong U, Chaiyaratana N, Tongpadungrod R (2007) Genetic programming and neural networks as interpreters for a distributive tactile sensing system. In: IEEE congress on evolutionary computation
39.
go back to reference Wu HC (2010) Duality theory for optimization problems with interval-valued objective functions. J Optim Theory Appl 144(3):615–628MathSciNetCrossRef Wu HC (2010) Duality theory for optimization problems with interval-valued objective functions. J Optim Theory Appl 144(3):615–628MathSciNetCrossRef
40.
go back to reference Ishibuchi H, Tanaka H (1990) Multiobjective programming in optimization of the interval objective function. Eur J Oper Res 48(2):219–225CrossRef Ishibuchi H, Tanaka H (1990) Multiobjective programming in optimization of the interval objective function. Eur J Oper Res 48(2):219–225CrossRef
41.
go back to reference Kinderlehrer D, Stampacchia G (2012) An introduction to variational inequalities and their applications. Academic Kinderlehrer D, Stampacchia G (2012) An introduction to variational inequalities and their applications. Academic
42.
go back to reference Xu D, Xia Y, Mandic DP (2016) Optimization in quaternion dynamic systems: gradient, hessian, and learning algorithms. IEEE Trans Neural Netw Learn Syst Sons 27(2):249–261MathSciNetCrossRef Xu D, Xia Y, Mandic DP (2016) Optimization in quaternion dynamic systems: gradient, hessian, and learning algorithms. IEEE Trans Neural Netw Learn Syst Sons 27(2):249–261MathSciNetCrossRef
43.
go back to reference Ghadimi S, Lan G, Zhang H (2019) Generalized uniformly optimal methods for nonlinear programming. J Sci Comput 79:1854–1881MathSciNetCrossRef Ghadimi S, Lan G, Zhang H (2019) Generalized uniformly optimal methods for nonlinear programming. J Sci Comput 79:1854–1881MathSciNetCrossRef
45.
go back to reference Fukushima M (1992) Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems. Math Program 53(1–3):99–110MathSciNetCrossRef Fukushima M (1992) Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems. Math Program 53(1–3):99–110MathSciNetCrossRef
46.
go back to reference Pang JS (2017) A posteriori error bounds for the linearly-constrained variational inequality problem. Math Oper Res 12(3):474–484MathSciNetCrossRef Pang JS (2017) A posteriori error bounds for the linearly-constrained variational inequality problem. Math Oper Res 12(3):474–484MathSciNetCrossRef
47.
go back to reference Qin S, Xue X (2015) A two-layer recurrent neural network for nonsmooth convex optimization problems. IEEE Trans Neural Netw Learn Syst 26(6):1149MathSciNetCrossRef Qin S, Xue X (2015) A two-layer recurrent neural network for nonsmooth convex optimization problems. IEEE Trans Neural Netw Learn Syst 26(6):1149MathSciNetCrossRef
48.
go back to reference Boese FG (2015) On the asymptotical stability of multivariate dynamical systems. PAMM 1(1):107–108CrossRef Boese FG (2015) On the asymptotical stability of multivariate dynamical systems. PAMM 1(1):107–108CrossRef
49.
go back to reference Bertsekas, D, Tsitsiklis J (2010) Parallel and distributed computation: numerical methods. Computer Science Bertsekas, D, Tsitsiklis J (2010) Parallel and distributed computation: numerical methods. Computer Science
Metadata
Title
A One-Layer Recurrent Neural Network for Interval-Valued Optimization Problem with Linear Constraints
Authors
Yueqiu Li
Chunna Zeng
Bing Li
Jin Hu
Publication date
03-01-2022
Publisher
Springer US
Published in
Neural Processing Letters / Issue 2/2022
Print ISSN: 1370-4621
Electronic ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-021-10681-w

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