Juyoung Jeong - Academia.edu (original) (raw)

Papers by Juyoung Jeong

arXiv (Cornell University), Aug 17, 2020

Given a linear map T on a Euclidean Jordan algebra of rank n, we consider the set of all nonnegat... more Given a linear map T on a Euclidean Jordan algebra of rank n, we consider the set of all nonnegative vectors q in R n with decreasing components that satisfy the pointwise weak-majorization inequality λ(|T (x)|) ≺ w q * λ(|x|), where λ is the eigenvalue map and * denotes the componentwise product in R n. With respect to the weak-majorization ordering, we show the existence of the least vector in this set. When T is a positive map, the least vector is shown to be the join (in the weak-majorization order) of eigenvalue vectors of T (e) and T * (e), where e is the unit element of the algebra. These results are analogous to the results of Bapat [4], proved in the setting of the space of all n × n complex matrices with singular value map in place of the eigenvalue map. They also extend two recent results of Tao, Jeong, and Gowda [21] proved for quadratic representations and Schur product induced transformations. As an application, we provide an estimate on the norm of a general linear map relative to spectral norms.

arXiv (Cornell University), Sep 28, 2022

arXiv (Cornell University), May 4, 2018

Let V be a Euclidean Jordan algebra of rank n. A set E in V is said to be a spectral set if there... more Let V be a Euclidean Jordan algebra of rank n. A set E in V is said to be a spectral set if there exists a permutation invariant set Q in R n such that E = λ −1 (Q), where λ : V → R n is the eigenvalue map that takes x ∈ V to λ(x) (the vector of eigenvalues of x written in the decreasing order). If the above Q is also a convex cone, we say that E is a spectral cone. This paper deals with connectedness and arcwise connectedness properties of spectral sets. By relying on the result that in a simple Euclidean Jordan algebra, every eigenvalue orbit [x] := {y : λ(y) = λ(x)} is arcwise connected, we show that if a permutation invariant set Q is connected (arcwise connected), then λ −1 (Q) is connected (respectively, arcwise connected). A related result is that in a simple Euclidean Jordan algebra, every pointed spectral cone is irreducible.

arXiv (Cornell University), Sep 28, 2022

A Fan-Theobald-von Neumann system [14] is a triple (V, W, λ), where V and W are real inner produc... more A Fan-Theobald-von Neumann system [14] is a triple (V, W, λ), where V and W are real inner product spaces and λ : V → W is a norm-preserving map satisfying a Fan-Theobald-von Neumann type inequality together with a condition for equality. Examples include Euclidean Jordan algebras, systems induced by certain hyperbolic polynomials, and normal decompositions systems (Eaton triples). In [14], we presented some basic properties of such systems and described results on optimization problems dealing with certain combinations of linear/distance and spectral functions. We also introduced the concept of commutativity via the equality in the Fan-Theobald-von Neumann type inequality. In the present paper, we elaborate on the concept of commutativity and introduce/study automorphisms, majorization, and reduction in Fan-Theobald-von Neumann systems.

arXiv (Cornell University), Apr 15, 2016

The commutation principle of Ramirez, Seeger, and Sossa [13] proved in the setting of Euclidean J... more The commutation principle of Ramirez, Seeger, and Sossa [13] proved in the setting of Euclidean Jordan algebras says that when the sum of a Fréchet differentiable function Θ(x) and a spectral function F (x) is minimized over a spectral set Ω, any local minimizer a operator commutes with the Fréchet derivative Θ ′ (a). In this paper, we extend this result to sets and functions which are (just) invariant under algebra automorphisms. We also consider a similar principle in the setting of normal decomposition systems.

IEEE Access, 2022

A hybrid-triggered controller is designed in this article to analyze the stabilization of parabol... more A hybrid-triggered controller is designed in this article to analyze the stabilization of parabolic type partial differential equations (PDEs) with deception attacks and disturbances. The hybrid-triggered controller is designed by combining time-triggered and event-triggered controllers with the aid of a Bernoulli random variable. A nonlinear function is considered to describe the deception attack signal and the probability of occurrence of deception attack signals will be determined by a Bernoulli random variable. An H ∞ performance is utilized to attenuate the occurrence disturbances. We employ a Lyapunov-Krasovskii functional (LKF) to analyze the stabilization of the chosen PDE under the proposed controller and the stabilization conditions are obtained in terms of linear matrix inequalities (LMIs). Numerical examples are given finally to check the efficacy of the derived results. INDEX TERMS Parabolic PDE, hybrid-triggered, deception attack, H ∞ control.

arXiv (Cornell University), Jul 17, 2023

A Fan-Theobald-von Neumann system [7] is a triple (V, W, λ), where V and W are real inner product... more A Fan-Theobald-von Neumann system [7] is a triple (V, W, λ), where V and W are real inner product spaces and λ : V → W is a norm-preserving map satisfying a Fan-Theobald-von Neumann type inequality together with a condition for equality. Examples include Euclidean Jordan algebras, systems induced by certain hyperbolic polynomials, and normal decomposition systems (Eaton triples). The present article is a continuation of [9] where the concepts of commutativity, automorphisms, majorization, and reduction were introduced and elaborated. Here, we describe some transfer principles and present Fenchel conjugate and subdifferential formulas.

arXiv (Cornell University), Aug 10, 2017

The Lyapunov rank of a proper cone K in a finite dimensional real Hilbert space is defined as the... more The Lyapunov rank of a proper cone K in a finite dimensional real Hilbert space is defined as the dimension of the space of all Lyapunov-like transformations on K, or equivalently, the dimension of the Lie algebra of the automorphism group of K. This (rank) measures the number of linearly independent bilinear relations needed to express a complementarity system on K (that arises, for example, from a linear program or a complementarity problem on the cone). Motivated by the problem of describing spectral/proper cones where the complementarity system can be expressed as a square system (that is, where the Lyapunov rank is greater than equal to the dimension of the ambient space), we consider proper polyhedral cones in R n that are permutation invariant. For such cones we show that the Lyapunov rank is either 1 (in which case, the cone is irreducible) or n (in which case, the cone is isomorphic to R n +). In the latter case, we show that the corresponding spectral cone is isomorphic to a symmetric cone.

Linear & Multilinear Algebra, Jan 7, 2021

Given a linear map T on a Euclidean Jordan algebra of rank n, we consider the set of all nonnegat... more Given a linear map T on a Euclidean Jordan algebra of rank n, we consider the set of all nonnegative vectors q in R n with decreasing components that satisfy the pointwise weak-majorization inequality λ(|T (x)|) ≺ w q * λ(|x|), where λ is the eigenvalue map and * denotes the componentwise product in R n. With respect to the weak-majorization ordering, we show the existence of the least vector in this set. When T is a positive map, the least vector is shown to be the join (in the weak-majorization order) of eigenvalue vectors of T (e) and T * (e), where e is the unit element of the algebra. These results are analogous to the results of Bapat [4], proved in the setting of the space of all n × n complex matrices with singular value map in place of the eigenvalue map. They also extend two recent results of Tao, Jeong, and Gowda [21] proved for quadratic representations and Schur product induced transformations. As an application, we provide an estimate on the norm of a general linear map relative to spectral norms.

Results in Mathematics

A Fan-Theobald-von Neumann system [14] is a triple (V, W, λ), where V and W are real inner produc... more A Fan-Theobald-von Neumann system [14] is a triple (V, W, λ), where V and W are real inner product spaces and λ : V → W is a norm-preserving map satisfying a Fan-Theobald-von Neumann type inequality together with a condition for equality. Examples include Euclidean Jordan algebras, systems induced by certain hyperbolic polynomials, and normal decompositions systems (Eaton triples). In [14], we presented some basic properties of such systems and described results on optimization problems dealing with certain combinations of linear/distance and spectral functions. We also introduced the concept of commutativity via the equality in the Fan-Theobald-von Neumann type inequality. In the present paper, we elaborate on the concept of commutativity and introduce/study automorphisms, majorization, and reduction in Fan-Theobald-von Neumann systems.

Applied Mathematics and Computation

International Journal of Nonlinear Sciences and Numerical Simulation

Trend filtering aims to estimate underlying trends in time series data, which is necessary to inv... more Trend filtering aims to estimate underlying trends in time series data, which is necessary to investigate data in a variety of disciplines. We propose a new method called elastic trend filtering. The proposed method combines ℓ 2 and ℓ 1 norm penalties to exploit the benefits and strengths of Hodrick–Prescott and ℓ 1 trend filterings. We apply the alternating direction method of multipliers for its efficient computation and numerical experiments show the soundness and efficiency of the proposed method. We further apply the proposed method to graph cases for potential applications and suggest a trend filtering for its variance estimate.

Communications in Nonlinear Science and Numerical Simulation

Linear and Multilinear Algebra

Linear Algebra and its Applications, 2020

In this paper, we extend the notion of weak majorization and doubly substochastic maps, and the H... more In this paper, we extend the notion of weak majorization and doubly substochastic maps, and the Hardy-Littlewood-Pólya theorem on majorization to Euclidean Jordan algebras. We also provide a characterization of doubly substochastic maps on Euclidean Jordan algebras in terms of Jordan algebra automorphisms and quadratic representations. In conjunction with that, various weak majorization inequalities of Aujla-Silva are generalized to Euclidean Jordan algebras.

Linear and Multilinear Algebra, 2020

Journal of Mathematical Analysis and Applications, 2018

The Lyapunov rank of a proper cone K in a finite dimensional real Hilbert space is defined as the... more The Lyapunov rank of a proper cone K in a finite dimensional real Hilbert space is defined as the dimension of the space of all Lyapunov-like transformations on K, or equivalently, the dimension of the Lie algebra of the automorphism group of K. This (rank) measures the number of linearly independent bilinear relations needed to express a complementarity system on K (that arises, for example, from a linear program or a complementarity problem on the cone). Motivated by the problem of describing spectral/proper cones where the complementarity system can be expressed as a square system (that is, where the Lyapunov rank is greater than equal to the dimension of the ambient space), we consider proper polyhedral cones in R n that are permutation invariant. For such cones we show that the Lyapunov rank is either 1 (in which case, the cone is irreducible) or n (in which case, the cone is isomorphic to R n +). In the latter case, we show that the corresponding spectral cone is isomorphic to a symmetric cone.

Linear Algebra and its Applications, 2017

SIAM Journal on Optimization, 2017

The commutation principle of Ramirez, Seeger, and Sossa [13] proved in the setting of Euclidean J... more The commutation principle of Ramirez, Seeger, and Sossa [13] proved in the setting of Euclidean Jordan algebras says that when the sum of a Fréchet differentiable function Θ(x) and a spectral function F (x) is minimized over a spectral set Ω, any local minimizer a operator commutes with the Fréchet derivative Θ ′ (a). In this paper, we extend this result to sets and functions which are (just) invariant under algebra automorphisms. We also consider a similar principle in the setting of normal decomposition systems.

Linear Algebra and its Applications, 2016

A spectral cone in a Euclidean Jordan algebra V of rank n is of the form K = λ −1 (Q), where Q is... more A spectral cone in a Euclidean Jordan algebra V of rank n is of the form K = λ −1 (Q), where Q is a permutation invariant convex cone in R n and λ : V → R n is the eigenvalue map (which takes x to λ(x), the vector of eigenvalues of x with entries written in the decreasing order). In this paper, we describe some properties of spectral cones. We show, for example, that spectral cones are invariant under automorphisms of V, that the dual of a spectral cone is a spectral cone when V is simple or carries the canonical inner product, and characterize the pointedness/solidness of a spectral cone. We also show that for any spectral cone K in V, dim(K) ∈ {0, 1, m − 1, m}, where dim(K) denotes the dimension of K and m is the dimension of V.

arXiv (Cornell University), Aug 17, 2020

Given a linear map T on a Euclidean Jordan algebra of rank n, we consider the set of all nonnegat... more Given a linear map T on a Euclidean Jordan algebra of rank n, we consider the set of all nonnegative vectors q in R n with decreasing components that satisfy the pointwise weak-majorization inequality λ(|T (x)|) ≺ w q * λ(|x|), where λ is the eigenvalue map and * denotes the componentwise product in R n. With respect to the weak-majorization ordering, we show the existence of the least vector in this set. When T is a positive map, the least vector is shown to be the join (in the weak-majorization order) of eigenvalue vectors of T (e) and T * (e), where e is the unit element of the algebra. These results are analogous to the results of Bapat [4], proved in the setting of the space of all n × n complex matrices with singular value map in place of the eigenvalue map. They also extend two recent results of Tao, Jeong, and Gowda [21] proved for quadratic representations and Schur product induced transformations. As an application, we provide an estimate on the norm of a general linear map relative to spectral norms.

arXiv (Cornell University), Sep 28, 2022

arXiv (Cornell University), May 4, 2018

Let V be a Euclidean Jordan algebra of rank n. A set E in V is said to be a spectral set if there... more Let V be a Euclidean Jordan algebra of rank n. A set E in V is said to be a spectral set if there exists a permutation invariant set Q in R n such that E = λ −1 (Q), where λ : V → R n is the eigenvalue map that takes x ∈ V to λ(x) (the vector of eigenvalues of x written in the decreasing order). If the above Q is also a convex cone, we say that E is a spectral cone. This paper deals with connectedness and arcwise connectedness properties of spectral sets. By relying on the result that in a simple Euclidean Jordan algebra, every eigenvalue orbit [x] := {y : λ(y) = λ(x)} is arcwise connected, we show that if a permutation invariant set Q is connected (arcwise connected), then λ −1 (Q) is connected (respectively, arcwise connected). A related result is that in a simple Euclidean Jordan algebra, every pointed spectral cone is irreducible.

arXiv (Cornell University), Sep 28, 2022

A Fan-Theobald-von Neumann system [14] is a triple (V, W, λ), where V and W are real inner produc... more A Fan-Theobald-von Neumann system [14] is a triple (V, W, λ), where V and W are real inner product spaces and λ : V → W is a norm-preserving map satisfying a Fan-Theobald-von Neumann type inequality together with a condition for equality. Examples include Euclidean Jordan algebras, systems induced by certain hyperbolic polynomials, and normal decompositions systems (Eaton triples). In [14], we presented some basic properties of such systems and described results on optimization problems dealing with certain combinations of linear/distance and spectral functions. We also introduced the concept of commutativity via the equality in the Fan-Theobald-von Neumann type inequality. In the present paper, we elaborate on the concept of commutativity and introduce/study automorphisms, majorization, and reduction in Fan-Theobald-von Neumann systems.

arXiv (Cornell University), Apr 15, 2016

The commutation principle of Ramirez, Seeger, and Sossa [13] proved in the setting of Euclidean J... more The commutation principle of Ramirez, Seeger, and Sossa [13] proved in the setting of Euclidean Jordan algebras says that when the sum of a Fréchet differentiable function Θ(x) and a spectral function F (x) is minimized over a spectral set Ω, any local minimizer a operator commutes with the Fréchet derivative Θ ′ (a). In this paper, we extend this result to sets and functions which are (just) invariant under algebra automorphisms. We also consider a similar principle in the setting of normal decomposition systems.

IEEE Access, 2022

A hybrid-triggered controller is designed in this article to analyze the stabilization of parabol... more A hybrid-triggered controller is designed in this article to analyze the stabilization of parabolic type partial differential equations (PDEs) with deception attacks and disturbances. The hybrid-triggered controller is designed by combining time-triggered and event-triggered controllers with the aid of a Bernoulli random variable. A nonlinear function is considered to describe the deception attack signal and the probability of occurrence of deception attack signals will be determined by a Bernoulli random variable. An H ∞ performance is utilized to attenuate the occurrence disturbances. We employ a Lyapunov-Krasovskii functional (LKF) to analyze the stabilization of the chosen PDE under the proposed controller and the stabilization conditions are obtained in terms of linear matrix inequalities (LMIs). Numerical examples are given finally to check the efficacy of the derived results. INDEX TERMS Parabolic PDE, hybrid-triggered, deception attack, H ∞ control.

arXiv (Cornell University), Jul 17, 2023

A Fan-Theobald-von Neumann system [7] is a triple (V, W, λ), where V and W are real inner product... more A Fan-Theobald-von Neumann system [7] is a triple (V, W, λ), where V and W are real inner product spaces and λ : V → W is a norm-preserving map satisfying a Fan-Theobald-von Neumann type inequality together with a condition for equality. Examples include Euclidean Jordan algebras, systems induced by certain hyperbolic polynomials, and normal decomposition systems (Eaton triples). The present article is a continuation of [9] where the concepts of commutativity, automorphisms, majorization, and reduction were introduced and elaborated. Here, we describe some transfer principles and present Fenchel conjugate and subdifferential formulas.

arXiv (Cornell University), Aug 10, 2017

The Lyapunov rank of a proper cone K in a finite dimensional real Hilbert space is defined as the... more The Lyapunov rank of a proper cone K in a finite dimensional real Hilbert space is defined as the dimension of the space of all Lyapunov-like transformations on K, or equivalently, the dimension of the Lie algebra of the automorphism group of K. This (rank) measures the number of linearly independent bilinear relations needed to express a complementarity system on K (that arises, for example, from a linear program or a complementarity problem on the cone). Motivated by the problem of describing spectral/proper cones where the complementarity system can be expressed as a square system (that is, where the Lyapunov rank is greater than equal to the dimension of the ambient space), we consider proper polyhedral cones in R n that are permutation invariant. For such cones we show that the Lyapunov rank is either 1 (in which case, the cone is irreducible) or n (in which case, the cone is isomorphic to R n +). In the latter case, we show that the corresponding spectral cone is isomorphic to a symmetric cone.

Linear & Multilinear Algebra, Jan 7, 2021

Given a linear map T on a Euclidean Jordan algebra of rank n, we consider the set of all nonnegat... more Given a linear map T on a Euclidean Jordan algebra of rank n, we consider the set of all nonnegative vectors q in R n with decreasing components that satisfy the pointwise weak-majorization inequality λ(|T (x)|) ≺ w q * λ(|x|), where λ is the eigenvalue map and * denotes the componentwise product in R n. With respect to the weak-majorization ordering, we show the existence of the least vector in this set. When T is a positive map, the least vector is shown to be the join (in the weak-majorization order) of eigenvalue vectors of T (e) and T * (e), where e is the unit element of the algebra. These results are analogous to the results of Bapat [4], proved in the setting of the space of all n × n complex matrices with singular value map in place of the eigenvalue map. They also extend two recent results of Tao, Jeong, and Gowda [21] proved for quadratic representations and Schur product induced transformations. As an application, we provide an estimate on the norm of a general linear map relative to spectral norms.

Results in Mathematics

A Fan-Theobald-von Neumann system [14] is a triple (V, W, λ), where V and W are real inner produc... more A Fan-Theobald-von Neumann system [14] is a triple (V, W, λ), where V and W are real inner product spaces and λ : V → W is a norm-preserving map satisfying a Fan-Theobald-von Neumann type inequality together with a condition for equality. Examples include Euclidean Jordan algebras, systems induced by certain hyperbolic polynomials, and normal decompositions systems (Eaton triples). In [14], we presented some basic properties of such systems and described results on optimization problems dealing with certain combinations of linear/distance and spectral functions. We also introduced the concept of commutativity via the equality in the Fan-Theobald-von Neumann type inequality. In the present paper, we elaborate on the concept of commutativity and introduce/study automorphisms, majorization, and reduction in Fan-Theobald-von Neumann systems.

Applied Mathematics and Computation

International Journal of Nonlinear Sciences and Numerical Simulation

Trend filtering aims to estimate underlying trends in time series data, which is necessary to inv... more Trend filtering aims to estimate underlying trends in time series data, which is necessary to investigate data in a variety of disciplines. We propose a new method called elastic trend filtering. The proposed method combines ℓ 2 and ℓ 1 norm penalties to exploit the benefits and strengths of Hodrick–Prescott and ℓ 1 trend filterings. We apply the alternating direction method of multipliers for its efficient computation and numerical experiments show the soundness and efficiency of the proposed method. We further apply the proposed method to graph cases for potential applications and suggest a trend filtering for its variance estimate.

Communications in Nonlinear Science and Numerical Simulation

Linear and Multilinear Algebra

Linear Algebra and its Applications, 2020

In this paper, we extend the notion of weak majorization and doubly substochastic maps, and the H... more In this paper, we extend the notion of weak majorization and doubly substochastic maps, and the Hardy-Littlewood-Pólya theorem on majorization to Euclidean Jordan algebras. We also provide a characterization of doubly substochastic maps on Euclidean Jordan algebras in terms of Jordan algebra automorphisms and quadratic representations. In conjunction with that, various weak majorization inequalities of Aujla-Silva are generalized to Euclidean Jordan algebras.

Linear and Multilinear Algebra, 2020

Journal of Mathematical Analysis and Applications, 2018

The Lyapunov rank of a proper cone K in a finite dimensional real Hilbert space is defined as the... more The Lyapunov rank of a proper cone K in a finite dimensional real Hilbert space is defined as the dimension of the space of all Lyapunov-like transformations on K, or equivalently, the dimension of the Lie algebra of the automorphism group of K. This (rank) measures the number of linearly independent bilinear relations needed to express a complementarity system on K (that arises, for example, from a linear program or a complementarity problem on the cone). Motivated by the problem of describing spectral/proper cones where the complementarity system can be expressed as a square system (that is, where the Lyapunov rank is greater than equal to the dimension of the ambient space), we consider proper polyhedral cones in R n that are permutation invariant. For such cones we show that the Lyapunov rank is either 1 (in which case, the cone is irreducible) or n (in which case, the cone is isomorphic to R n +). In the latter case, we show that the corresponding spectral cone is isomorphic to a symmetric cone.

Linear Algebra and its Applications, 2017

SIAM Journal on Optimization, 2017

The commutation principle of Ramirez, Seeger, and Sossa [13] proved in the setting of Euclidean J... more The commutation principle of Ramirez, Seeger, and Sossa [13] proved in the setting of Euclidean Jordan algebras says that when the sum of a Fréchet differentiable function Θ(x) and a spectral function F (x) is minimized over a spectral set Ω, any local minimizer a operator commutes with the Fréchet derivative Θ ′ (a). In this paper, we extend this result to sets and functions which are (just) invariant under algebra automorphisms. We also consider a similar principle in the setting of normal decomposition systems.

Linear Algebra and its Applications, 2016

A spectral cone in a Euclidean Jordan algebra V of rank n is of the form K = λ −1 (Q), where Q is... more A spectral cone in a Euclidean Jordan algebra V of rank n is of the form K = λ −1 (Q), where Q is a permutation invariant convex cone in R n and λ : V → R n is the eigenvalue map (which takes x to λ(x), the vector of eigenvalues of x with entries written in the decreasing order). In this paper, we describe some properties of spectral cones. We show, for example, that spectral cones are invariant under automorphisms of V, that the dual of a spectral cone is a spectral cone when V is simple or carries the canonical inner product, and characterize the pointedness/solidness of a spectral cone. We also show that for any spectral cone K in V, dim(K) ∈ {0, 1, m − 1, m}, where dim(K) denotes the dimension of K and m is the dimension of V.