Homotopy Method for a General Multiobjective Programming Problem

Song, Wen; Yao, Guangming

doi:10.1007/s10957-008-9366-6

Cited by 16 publications

(29 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In comparison with [21,27], the normal cone condition (A5) only requires that the constraint shifting set Ω(t) holds as t = 1 but not the whole constraint set Ω, and the initial point requires only in the shifted feasible set but not the original feasible set. Therefore, it is much weaker than that of [21,27].…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

A modified constraint shifting homotopy method for solving general nonlinear multiobjective programming

Zhu¹,

Yao²

2017

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

In this paper, for solving the general nonconvex multiobjective programming with both inequality and equality constraints, a modified constraint shifting homotopy is constructed, and the existence and global convergence of the smooth homotopy pathway is proven for any initial point in the almost Euclidean space under some mild conditions. The advantage of the newly proposed method requires that the initial point can be chosen much more conveniently, which needs to be only in the shifted feasible set not necessarily in the original feasible set. Meanwhile, the normal cone condition for proving the global convergence, which is much weaker than the existing interior method, need only be satisfied at the boundary of the shifted feasible set but not the original constraint set.

show abstract

Section: Resultsmentioning

confidence: 99%

“…In 2008, the combined homotopy interior point method was generalized to solve the general multiobjective programming problem under the so-called normal cone condition and the homotopy was constructed in [21] as follows:…”

Section: Introductionmentioning

confidence: 99%

A modified constraint shifting homotopy method for solving general nonlinear multiobjective programming

Zhu¹,

Yao²

2017

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

show abstract

“…In [9], a homotopy method for MOP with bounded  was given. In this paper, we will discuss MOP with  which is not necessarily bounded.…”

Section: Preliminariesmentioning

confidence: 99%

“…In 2008, Song and Yao [9] further generalized the results of [8,10]. They constructed a new combined homotopy mapping.…”

Section: Introductionmentioning

confidence: 99%

Homotopy Continuous Method for Weak Efficient Solution of Multiobjective Optimization Problem with Feasible Set Unbounded Condition

Wang¹,

Wu²

2012

View full text Add to dashboard Cite

In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.

show abstract

“…[1,14], we considered a combined homotopy interior point method for the multiobjective programming (MOP) under the condition linearly independent constraint qualification (LICQ). To find a KKT point of (MOP), we construct a homotopy as follows…”

Section: Introductionmentioning

confidence: 99%

A Weaker Constraint Qualification of Globally Convergent Homotopy Method for a Multiobjective Programming Problem

Yao

Song²

2013

View full text Add to dashboard Cite

In this paper, we prove that the combined homotopy interior point method for a multiobjective programming problem introduced in Ref.[1] remains valid under a weaker constrained qualification-the Mangasarian-Fromovitz constrained qualification, instead of linear independence constraint qualification. The algorithm generated by this method associated to the Karush-Kuhn-Tucker points of the multiobjective programming problem is proved to be globally convergent.

show abstract

Homotopy Method for a General Multiobjective Programming Problem

Cited by 16 publications

References 9 publications

A modified constraint shifting homotopy method for solving general nonlinear multiobjective programming

A modified constraint shifting homotopy method for solving general nonlinear multiobjective programming

Homotopy Continuous Method for Weak Efficient Solution of Multiobjective Optimization Problem with Feasible Set Unbounded Condition

A Weaker Constraint Qualification of Globally Convergent Homotopy Method for a Multiobjective Programming Problem

Contact Info

Product

Resources

About