Monotonicity and stability of optimal solutions of a minimization problem

Yichen Liu; Behrouz Emamizadeh

doi:10.1016/j.cnsns.2015.01.016

Monotonicity and stability of optimal solutions of a minimization problem

Yichen Liu^*, Behrouz Emamizadeh

^*Corresponding author for this work

Department of Applied Mathematics

Xi'an Jiaotong-Liverpool University

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

This paper is concerned with a minimization problem modeling the minimum displacement of an isotropic elastic membrane subject to a vertical force such as a load distribution. In addition to proving existence and uniqueness of optimal solutions, we show that these solutions are monotone and stable, in a certain sense. The main mathematical tool used in the analysis is the tangent cones from convex analysis, which helps to derive the optimality condition. Our results are compatible with physical expectations.

Original language	English
Pages (from-to)	94-101
Number of pages	8
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	25
Issue number	1-3
DOIs	https://doi.org/10.1016/j.cnsns.2015.01.016
Publication status	Published - 1 Aug 2015

Keywords

Displacement
Existence
Membrane
Monotonicity
Optimal solutions
Optimality conditions
Optimization
Stability
Tangent cones
Uniqueness

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10.1016/j.cnsns.2015.01.016

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author = "Yichen Liu and Behrouz Emamizadeh",

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AU - Emamizadeh, Behrouz

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AB - This paper is concerned with a minimization problem modeling the minimum displacement of an isotropic elastic membrane subject to a vertical force such as a load distribution. In addition to proving existence and uniqueness of optimal solutions, we show that these solutions are monotone and stable, in a certain sense. The main mathematical tool used in the analysis is the tangent cones from convex analysis, which helps to derive the optimality condition. Our results are compatible with physical expectations.

KW - Displacement

KW - Existence

KW - Membrane

KW - Monotonicity

KW - Optimal solutions

KW - Optimality conditions

KW - Optimization

KW - Stability

KW - Tangent cones

KW - Uniqueness

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EP - 101

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 1-3

ER -

Monotonicity and stability of optimal solutions of a minimization problem

Abstract

Keywords

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