A Modified q-BFGS Algorithm for Unconstrained Optimization

Lai, Kin Keung; Mishra, Shashi Kant; Sharma, Ravina; Sharma, Manjari; Ram, Bhagwat

doi:10.3390/math11061420

Cited by 7 publications

(3 citation statements)

References 32 publications

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“…A modified q-BFGS algorithm is proposed for nonlinear unconstrained optimization problems [20]. It uses a simple symmetric positive definite matrix and a new q-quasi-Newton equation to build an approximate q-Hessian.…”

Section: Literature Reviewmentioning

confidence: 99%

An Efficient Limited Memory Multi-Step Quasi-Newton Method

Moghrabi,

Hassan

2024

Mathematics

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This paper is dedicated to the development of a novel class of quasi-Newton techniques tailored to address computational challenges posed by memory constraints. Such methodologies are commonly referred to as “limited” memory methods. The method proposed herein showcases adaptability by introducing a customizable memory parameter governing the retention of historical data in constructing the Hessian estimate matrix at each iterative stage. The search directions generated through this novel approach are derived from a modified version closely resembling the full memory multi-step BFGS update, incorporating limited memory computation for a singular term to approximate matrix–vector multiplication. Results from numerical experiments, exploring various parameter configurations, substantiate the enhanced efficiency of the proposed algorithm within the realm of limited memory quasi-Newton methodologies category.

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Section: Literature Reviewmentioning

confidence: 99%

An Efficient Limited Memory Multi-Step Quasi-Newton Method

Moghrabi,

Hassan

2024

Mathematics

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“…There are various quasi-Newton algorithms, and in this paper, the L-BFGS algorithm is utilized [32][33][34] . This algorithm ensures a high success rate in obstacle avoidance and also exhibits good performance in terms of solving accuracy and restart loss.…”

Section: Numerical Solutionmentioning

confidence: 99%

Gradient-based autonomous obstacle avoidance trajectory planning for B-spline UAVs

Sun,

Ding

et al. 2024

Sci Rep

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Unmanned aerial vehicles (UAVs) have become the focus of current research because of their practicability in various scenarios. However, current local path planning methods often result in trajectories with numerous sharp or inflection points, which are not ideal for smooth UAV flight. This paper introduces a UAV path planning approach based on distance gradients. The key improvements include generating collision-free paths using collision information from initial trajectories and obstacles. Then, collision-free paths are subsequently optimized using distance gradient information. Additionally, a trajectory time adjustment method is proposed to ensure the feasibility and safety of the trajectory while prioritizing smoothness. The Limited-memory BFGS algorithm is employed to efficiently solve optimal local paths, with the ability to quickly restart the trajectory optimization program. The effectiveness of the proposed method is validated in the Robot Operating System simulation environment, demonstrating its ability to meet trajectory planning requirements for UAVs in complex unknown environments with high dynamics. Moreover, it surpasses traditional UAV trajectory planning methods in terms of solution speed, trajectory length, and data volume.

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“…In the Literature Review section, we have seen that there are variants of methods to show the faster convergence. However, quantum derivative has only been used and the problems have only been solved through very limited methods [10,13,14,33,34]. We aim to open doors for this exciting research area, where quantum calculus will help to solve problems with the least number of iterations-the quantum spectral gradient that provides a quantum descent direction at every iteration.…”

Section: Literature Reviewmentioning

confidence: 99%

A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems

Lai,

Mishra,

Ram

et al. 2023

Mathematics

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Quantum computing is an emerging field that has had a significant impact on optimization. Among the diverse quantum algorithms, quantum gradient descent has become a prominent technique for solving unconstrained optimization (UO) problems. In this paper, we propose a quantum spectral Polak–Ribiére–Polyak (PRP) conjugate gradient (CG) approach. The technique is considered as a generalization of the spectral PRP method which employs a q-gradient that approximates the classical gradient with quadratically better dependence on the quantum variable q. Additionally, the proposed method reduces to the classical variant as the quantum variable q approaches closer to 1. The quantum search direction always satisfies the sufficient descent condition and does not depend on any line search (LS). This approach is globally convergent with the standard Wolfe conditions without any convexity assumption. Numerical experiments are conducted and compared with the existing approach to demonstrate the improvement of the proposed strategy.

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A Modified q-BFGS Algorithm for Unconstrained Optimization

Cited by 7 publications

References 32 publications

An Efficient Limited Memory Multi-Step Quasi-Newton Method

An Efficient Limited Memory Multi-Step Quasi-Newton Method

Gradient-based autonomous obstacle avoidance trajectory planning for B-spline UAVs

A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems

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