The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
이 논문은 최적의 하한을 구성하는 문제에 대한 폐쇄형 솔루션을 제시합니다. 볼록한 특정 조건에서 작동합니다. 함수는 (I) -ρ에 의해 아래로 묶여 있다고 가정하고 (II) 미분 가능하며 그 도함수는 다음과 같습니다. Lipschitz 상수 L을 갖는 연속 Lipschitz. 하한을 구성하기 위해 ρ 값과 ρ 값을 사용할 수 있다고 가정합니다. L 지정된 하나의 지점에서 함수 및 그 파생 값의 값과 함께. 제안된 하한을 사용하여 계산적으로 효율적인 심층을 도출합니다. 단조 근사 연산자 부터 레벨 세트 기능의. 이 연산자는 다음보다 더 나은 근사치를 실현합니다. 하위 경사 투영 이는 미분 가능한 볼록 함수뿐만 아니라 매끄럽지 않은 볼록 함수의 레벨 세트에 대한 단조 근사 연산자로 활용되었습니다. 따라서 제안된 연산자를 사용하면 본질적으로 하위 경사 투영을 기반으로 하는 많은 신호 처리 알고리즘을 향상시킬 수 있습니다.
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Masao YAMAGISHI, Isao YAMADA, "A Deep Monotone Approximation Operator Based on the Best Quadratic Lower Bound of Convex Functions" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 8, pp. 1858-1866, August 2008, doi: 10.1093/ietfec/e91-a.8.1858.
Abstract: This paper presents a closed form solution to a problem of constructing the best lower bound of a convex function under certain conditions. The function is assumed (I) bounded below by -ρ, and (II) differentiable and its derivative is Lipschitz continuous with Lipschitz constant L. To construct the lower bound, it is also assumed that we can use the values ρ and L together with the values of the function and its derivative at one specified point. By using the proposed lower bound, we derive a computationally efficient deep monotone approximation operator to the level set of the function. This operator realizes better approximation than subgradient projection which has been utilized, as a monotone approximation operator to level sets of differentiable convex functions as well as nonsmooth convex functions. Therefore, by using the proposed operator, we can improve many signal processing algorithms essentially based on the subgradient projection.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.8.1858/_p
부
@ARTICLE{e91-a_8_1858,
author={Masao YAMAGISHI, Isao YAMADA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Deep Monotone Approximation Operator Based on the Best Quadratic Lower Bound of Convex Functions},
year={2008},
volume={E91-A},
number={8},
pages={1858-1866},
abstract={This paper presents a closed form solution to a problem of constructing the best lower bound of a convex function under certain conditions. The function is assumed (I) bounded below by -ρ, and (II) differentiable and its derivative is Lipschitz continuous with Lipschitz constant L. To construct the lower bound, it is also assumed that we can use the values ρ and L together with the values of the function and its derivative at one specified point. By using the proposed lower bound, we derive a computationally efficient deep monotone approximation operator to the level set of the function. This operator realizes better approximation than subgradient projection which has been utilized, as a monotone approximation operator to level sets of differentiable convex functions as well as nonsmooth convex functions. Therefore, by using the proposed operator, we can improve many signal processing algorithms essentially based on the subgradient projection.},
keywords={},
doi={10.1093/ietfec/e91-a.8.1858},
ISSN={1745-1337},
month={August},}
부
TY - JOUR
TI - A Deep Monotone Approximation Operator Based on the Best Quadratic Lower Bound of Convex Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1858
EP - 1866
AU - Masao YAMAGISHI
AU - Isao YAMADA
PY - 2008
DO - 10.1093/ietfec/e91-a.8.1858
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E91-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2008
AB - This paper presents a closed form solution to a problem of constructing the best lower bound of a convex function under certain conditions. The function is assumed (I) bounded below by -ρ, and (II) differentiable and its derivative is Lipschitz continuous with Lipschitz constant L. To construct the lower bound, it is also assumed that we can use the values ρ and L together with the values of the function and its derivative at one specified point. By using the proposed lower bound, we derive a computationally efficient deep monotone approximation operator to the level set of the function. This operator realizes better approximation than subgradient projection which has been utilized, as a monotone approximation operator to level sets of differentiable convex functions as well as nonsmooth convex functions. Therefore, by using the proposed operator, we can improve many signal processing algorithms essentially based on the subgradient projection.
ER -