Duality theorems and saddle point optimality conditions in fuzzy nonlinear programming problems based on different solution concepts

Duality theorem is an attractive approach for solving fuzzy optimization problems. However, the duality gap is generally nonzero for nonconvex problems. So far, most of the studies focus on continuous variables in fuzzy optimization problems. And, in real problems and models, fuzzy optimization problems also involve discrete and mixed variables. To address the above problems, we improve the extended duality theory by adding fuzzy objective functions. In this paper, we first define continuous fuzzy nonlinear programming problems, discrete fuzzy nonlinear programming problems, and mixed fuzzy nonlinear programming problems and then provide the extended dual problems, respectively. Finally we prove the weak and strong extended duality theorems, and the results show no duality gap between the original problem and extended dual problem.

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Optimality conditions for invex interval valued nonlinear programming problems involving generalized H-derivative

Filomat ◽

10.2298/fil1608121a ◽

2016 ◽

Vol 30 (8) ◽

pp. 2121-2138 ◽

Cited By ~ 2

Author(s):

Izhar Ahmad ◽

Deepak Singh ◽

Bilal Dar

Keyword(s):

Nonlinear Programming ◽

Optimality Conditions ◽

Generalized Convexity ◽

Optimal Solutions ◽

Solution Concepts ◽

Lagrangian Multipliers ◽

Kkt Optimality Conditions ◽

Generalized Hukuhara Differentiability ◽

Interval Valued

In this paper, some interval valued programming problems are discussed. The solution concepts are adopted from Wu [7] and Chalco-Cano et al. [34]. By considering generalized Hukuhara differentiability and generalized convexity (viz. ?-preinvexity, ?-invexity etc.) of interval valued functions, the KKT optimality conditions for obtaining (LS and LU) optimal solutions are elicited by introducing Lagrangian multipliers. Our results generalize the results of Wu [7], Zhang et al. [11] and Chalco-Cano et al. [34]. To illustrate our theorems suitable examples are also provided

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On semidifferentiable interval-valued programming problems

Journal of Inequalities and Applications ◽

10.1186/s13660-021-02566-2 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Kin Keung Lai ◽

Avanish Shahi ◽

Shashi Kant Mishra

Keyword(s):

Saddle Point ◽

Optimality Conditions ◽

Minimization Problem ◽

Optimal Solution ◽

Optimality Criteria ◽

Lagrangian Function ◽

Sufficient Optimality Conditions ◽

Duality Theorems ◽

Preinvex Functions ◽

Interval Valued

AbstractIn this paper, we consider the semidifferentiable case of an interval-valued minimization problem and establish sufficient optimality conditions and Wolfe type as well as Mond–Weir type duality theorems under semilocal E-preinvex functions. Furthermore, we present saddle-point optimality criteria to relate an optimal solution of the semidifferentiable interval-valued programming problem and a saddle point of the Lagrangian function.

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A QFD-Based Quality and Capability Design Method for Transboundary Services

Mathematical Problems in Engineering ◽

10.1155/2020/9478083 ◽

2020 ◽

Vol 2020 ◽

pp. 1-18 ◽

Cited By ~ 1

Author(s):

Chao Ma ◽

Wei Dong Liu ◽

Zhi Ying Tu ◽

Zhong Jie Wang ◽

Xiao Fei Xu

Keyword(s):

Nonlinear Programming ◽

Quality Function Deployment ◽

Design Method ◽

Quality Parameters ◽

Optimal Configuration ◽

Two Phase ◽

Internet Service ◽

Fuzzy Nonlinear Programming ◽

Nonlinear Programming Methods ◽

Multiple Domains

The “transboundary”, an emerging phenomenon in the Internet service ecosystem, is leading to the flourishing of innovative services. A transboundary service incorporates services, resources, and technologies from multiple domains into its business to create a particular competitive advantage and unique user experiences. It is difficult to comprehensively consider all the constraints from multiple domains to precisely design the nonfunctional characteristics of transboundary services, such as quality attributes and capability attributes. We propose a two-phase quality design method for transboundary services called value quality deployment-quality capability deployment (VQD-QCD) based on quality function deployment (QFD). Given the restrictions of transboundary services, VQD-QCD translates the value expectations of multiple stakeholders into an optimal configuration for global quality parameters (GQPs), local quality parameters, and capability parameters. Details of VQD are illustrated. Considering the inherent vagueness and uncertainty of relationships between value expectations and GQPs, and among GQPs, fuzzy least absolute regression and fuzzy nonlinear programming methods are incorporated into QFD to identify the quantitative relations between value indicators and GQPs, and among GQPs, and obtain an optimal configuration scheme for GQPs. Usability of the proposed method is validated through a case study on the “DiDi mobile transportation service”, which is a representative transboundary service in China. Compared with the current method, which is inaccurate and inefficient because its translation between value expectations and relevant quality and capability parameters is artificial and subjective, the proposed method integrates fuzzy least absolute regression and fuzzy nonlinear programming methods into QFD, which facilitate transboundary service designers to precisely and efficiently design the quality and capability characteristics of innovative services in the manner of semiautomatisation, which promotes the innovative design of transboundary services.

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