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Deep Neural Networks for Image-Based Dietary Assessment

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Published on: March 13, 2021

A modified subgradient extragradient method for solving monotone variational inequalities.

Songnian He^1,2, Tao Wu¹

¹College of Science, Civil Aviation University of China, Tianjin, 300300 China.

Journal of Inequalities and Applications

|May 19, 2017

Summary

This summary is machine-generated.

This study introduces a new adaptive method for solving variational inequalities in Hilbert spaces. The algorithm demonstrates weak convergence and a specific convergence rate, offering an efficient approach for complex mathematical problems.

Keywords:

Lipschitz-continuous mapping convergence rate half-spaces level set subgradient extragradient method variational inequalities

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Deep Neural Networks for Image-Based Dietary Assessment

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

Area of Science:

Optimization Theory
Functional Analysis
Numerical Analysis

Background:

Variational inequalities are fundamental in modeling various problems in applied mathematics and economics.
Existing methods for solving variational inequalities often require strong assumptions or complex computations.
The need for efficient and robust algorithms for monotone and Lipschitz-continuous problems persists.

Purpose of the Study:

To propose a novel, relaxed, and self-adaptive subgradient extragradient method.
To solve Lipschitz-continuous and monotone variational inequalities within a Hilbert space framework.
To analyze the convergence properties of the proposed iterative algorithm.

Main Methods:

Developing a modified subgradient extragradient iterative process.
Incorporating two metric projections onto half-spaces in each iteration.
Utilizing adaptive step size selection strategies.
Proving a weak convergence theorem for the algorithm.

Main Results:

The proposed algorithm converges weakly to a solution.
The method achieves a convergence rate of [Formula: see text].
The iterative process is computationally efficient due to relaxed and self-adaptive steps.

Conclusions:

The developed method provides an effective tool for solving a specific class of variational inequalities.
The adaptive nature of the algorithm enhances its practical applicability.
The proven convergence properties validate the theoretical soundness of the proposed approach.