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Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
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Updated: Jan 8, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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Augmenting Iterative Trajectory for Bilevel Optimization: Methodology, Analysis and Extensions.

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    This summary is machine-generated.

    This study introduces Augmented Iterative Trajectory (AIT) to improve Bi-Level Optimization (BLO) by addressing issues in hyper-gradient calculation and lower-level trajectories. AIT enhances convergence for various BLO scenarios, including non-convex problems.

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    Area of Science:

    • Machine Learning
    • Optimization

    Background:

    • Bi-Level Optimization (BLO) is crucial for hierarchical machine learning structures.
    • Existing gradient-based methods often neglect the interplay between hyper-gradient computation and lower-level (LL) trajectories, leading to convergence issues under restrictive assumptions.

    Purpose of the Study:

    • To analyze and address deficiencies in current Bi-Level Optimization (BLO) methods, specifically concerning initialization and hyper-gradient calculation.
    • To develop an Augmented Iterative Trajectory (AIT) approach for improved BLO performance across diverse scenarios.

    Main Methods:

    • Introduced Initialization Auxiliary (IA) and Pessimistic Trajectory Truncation (PTT) techniques.
    • Developed Augmented Iterative Trajectory (AIT) by incorporating prior regularization, varied iterative mapping, and acceleration dynamics.
    • Provided theoretical convergence analysis for AIT, including non-convex LL subproblems.

    Main Results:

    • Demonstrated the effectiveness of AIT through numerical examples.
    • Showcased AIT's applicability in data hyper-cleaning, few-shot learning, and neural architecture search.

    Conclusions:

    • The proposed AIT framework offers a robust solution for Bi-Level Optimization (BLO) challenges.
    • AIT improves convergence guarantees and practical performance, particularly for non-convex lower-level problems in machine learning applications.