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

Research output: Journal Publication › 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
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Numerical Analysis
Modelling and Simulation
Applied Mathematics

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10.1016/j.cnsns.2015.01.016

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title = "Monotonicity and stability of optimal solutions of a minimization problem",

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.",

keywords = "Displacement, Existence, Membrane, Monotonicity, Optimal solutions, Optimality conditions, Optimization, Stability, Tangent cones, Uniqueness",

author = "Yichen Liu and Behrouz Emamizadeh",

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AU - Liu, Yichen

AU - Emamizadeh, Behrouz

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N2 - 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.

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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M3 - Article

AN - SCOPUS:84924707272

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VL - 25

SP - 94

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

ASJC Scopus subject areas

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