Generalized Lagrange Function and Generalized Weak Saddle Points for a Class of Multiobjective Fractional Optimal Control Problems

Liu, Haijun; Fan, Neng; Pardalos, Pãnos M.

doi:10.1007/s10957-012-0007-8

Cited by 3 publications

(2 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many economic, noneconomic and indirect applications of FP problems have also been given by Craven [1] and Schaible and Ibaraki [2]. An extensive review and bibliography of the entire field of FP can be seen in [3][4][5][6][7][8][9][10]. Among them, Busygin et al [3] applied an interesting application of FP in data analysis.…”

Section: Introductionmentioning

confidence: 99%

“…Among them, Busygin et al [3] applied an interesting application of FP in data analysis. By constructing a kind of generalized Lagrange function for a class of multi-objective fractional optimal control problems, Liu et al [4] established sufficient and necessary conditions for existence of generalized weak saddle points. Pardalos and Phillips [5] discussed Dinkelbach's global optimization approach for finding the global maximum of the FP problems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A practical nonlinear dynamic framework for solving a class of fractional programming problems

Nazemi

Tahmasbi

2015

Nonlinear Dyn

View full text Add to dashboard Cite

In this paper, we present a highperformance dynamic optimization scheme to solve a class of fractional programming (FP) problems. The main idea is to convert the FP problem into an equivalent convex second-order cone programming problem. A neural network model based on a dynamic model is then constructed for solving the obtained convex programming problem. By employing a credible Lyapunov function approach, it is shown that the proposed neural network model is stable in the sense of Lyapunov and is globally convergent to an exact optimal solution of the original optimization problem. A block diagram of the model is also given. Several illustrative examples are provided to show the efficiency of the proposed method in this manuscript.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A practical nonlinear dynamic framework for solving a class of fractional programming problems

Nazemi

Tahmasbi

2015

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

Continuous Multiobjective Programming

Wiecek

Ehrgott

Engau

2016

Multiple Criteria Decision Analysis

View full text Add to dashboard Cite

Max–min distance nonnegative matrix factorization

Wang

Gao

2015

Neural Networks

View full text Add to dashboard Cite

Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problems. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basis matrix and a nonnegative coefficient matrix. The columns of the coefficient matrix can be used as new representations of these data samples. However, traditional NMF methods ignore class labels of the data samples. In this paper, we propose a novel supervised NMF algorithm to improve the discriminative ability of the new representation by using the class labels. Using the class labels, we separate all the data sample pairs into within-class pairs and between-class pairs. To improve the discriminative ability of the new NMF representations, we propose to minimize the maximum distance of the within-class pairs in the new NMF space, and meanwhile to maximize the minimum distance of the between-class pairs. With this criterion, we construct an objective function and optimize it with regard to basis and coefficient matrices, and slack variables alternatively, resulting in an iterative algorithm. The proposed algorithm is evaluated on three pattern classification problems and experiment results show that it outperforms the state-of-the-art supervised NMF methods.

show abstract

Generalized Lagrange Function and Generalized Weak Saddle Points for a Class of Multiobjective Fractional Optimal Control Problems

Cited by 3 publications

References 14 publications

A practical nonlinear dynamic framework for solving a class of fractional programming problems

A practical nonlinear dynamic framework for solving a class of fractional programming problems

Continuous Multiobjective Programming

Max–min distance nonnegative matrix factorization

Contact Info

Product

Resources

About