Trust Region Research Articles

Multi-Batch Carrier-Based UAV Formation Rendezvous Method Based on Improved Sequential Convex Programming

The limitations of the existing catapults necessitate multiple batches of take-offs for carrier-based unmanned aerial vehicles (UAVs) to form a formation. Because of the differences in takeoff time and location of each batch of UAVs, ensuring the temporal and spatial consistency and rendezvous efficiency of the formation becomes crucial. Concerning the challenges mentioned above, a multi-batch formation rendezvous method based on improved sequential convex programming (SCP) is proposed. A reverse solution approach based on the multi-batch rendezvous process is developed. On this basis, a non-convex optimization problem is formulated considering the following constraints: UAV dynamics, collision avoidance, obstacle avoidance, and formation consistency. An SCP method that makes use of the trust region strategy is introduced to solve the problem efficiently. Due to the spatiotemporal coupling characteristics of the rendezvous process, an inappropriate initial solution for SCP will inevitably reduce the rendezvous efficiency. Thus, an initial solution tolerance mechanism is introduced to improve the SCP. This mechanism follows the idea of simulated annealing, allowing the SCP to search for better reference solutions in a wider space. By utilizing the initial solution tolerance SCP (IST-SCP), the multi-batch formation rendezvous algorithm is developed correspondingly. Simulation results are obtained to verify the effectiveness and adaptability of the proposed method. IST-SCP reduces the rendezvous time from poor initial solutions without significantly increasing the computing time.

The mixed integer trust region problem

The mixed integer trust region problem

A trust region algorithm for finite-strain plasticity with strongly coupled hardening

As extensions to our Lagrangian finite-strain plasticity framework based on the approximate exponential integrator, we introduce two new algorithms: (i) a fixed-radius trust region root finder for the nonlinear system involving the elastic right Cauchy Green tensor and plastic multiplier (ii) a partitioned approach for the hardening variables, which are determined in a staggered form using the strongly-coupled concept typically adopted for multiphysics problems. This allows the use of intricate hyperelastic laws combined with recent yield functions, which otherwise would involve a laborious treatment, and the use of corresponding work-hardening. Work-hardening would introduce significant nonlinearities in the constitutive system if used in a fully-coupled form. For the partitioned approach, a dynamic relaxation algorithm is adopted. This allows the efficient solution of the two nonlinear equations without significant drifting. Results show that robustness and efficiency are significantly improved. Herein, algorithms are described in detail. Significant testing is performed with imposed strains up to 100 for a carbon steel. This contributes to the robustness of equilibrium iterations. Drifting is also assessed as a function of number of steps in the dynamic relaxation algorithm. Numerical experimentation is performed in the 3D tension test for an anisotropic yield function.

Priority-based intelligent resolution method of multi-aircraft flight conflicts

Abstract The rising demand for air traffic will inevitably result in a surge in both the number and complexity of flight conflicts, necessitating intelligent strategies for conflict resolution. This study addresses the critical challenges of scalability and real-time performance in multi-aircraft flight conflict resolution by proposing a comprehensive method that integrates a priority ranking mechanism with a conflict resolution model based on the Markov decision process (MDP). Within this framework, the proximity between aircraft in a multi-aircraft conflict set is dynamically assessed to establish a conflict resolution ranking mechanism. The problem of multi-aircraft conflict resolution is formalised through the MDP, encompassing the design of state space, discrete action space and reward function, with the transition function implemented via simulation prediction using model-free methods. To address the positional uncertainty of aircraft in real-time scenarios, the conflict detection mechanism introduces the aircraft’s positional error. A deep reinforcement learning (DRL) environment is constructed incorporating actual airspace structures and traffic densities, leveraging the Actor Critic using Kronecker-factored Trust Region (ACKTR) algorithm to determine resolution actions. The experimental results indicate that with 20–30 aircraft in the airspace, the success rate can reach 94% for the training set and 85% for the test set. Furthermore, this study analyses the impact of varying aircraft numbers on the success rate within a specific airspace scenario. The outcomes of this research provide valuable insights for the automation of flight conflict resolution.

PDFO: a cross-platform package for Powell’s derivative-free optimization solvers

AbstractThe late Professor M. J. D. Powell devised five trust-region methods for derivative-free optimization, namely COBYLA, UOBYQA, NEWUOA, BOBYQA, and LINCOA. He carefully implemented them into publicly available solvers, renowned for their robustness and efficiency. However, the solvers were implemented in Fortran 77 and hence may not be easily accessible to some users. We introduce the PDFO package, which provides user-friendly Python and MATLAB interfaces to Powell’s code. With PDFO, users of such languages can call Powell’s Fortran solvers easily without dealing with the Fortran code. Moreover, PDFO includes bug fixes and improvements, which are particularly important for handling problems that suffer from ill-conditioning or failures of function evaluations. In addition to the PDFO package, we provide an overview of Powell’s methods, sketching them from a uniform perspective, summarizing their main features, and highlighting the similarities and interconnections among them. We also present experiments on PDFO to demonstrate its stability under noise, tolerance of failures in function evaluations, and potential to solve certain hyperparameter optimization problems.

Multi‐criteria hydraulic turbine optimization using a genetic algorithm and trust‐region postprocessing

AbstractA two‐stage, multi‐objective optimization approach is proposed to improve the overall efficiency of the time‐consuming and computationally expensive optimization process for hydraulic turbines. The purpose is to optimize the shape of the turbine blades, designed using 30 parameters, in order to maximize its efficiency and minimize both the cavitation volume and the deviation between the desired and the calculated design head. In the first step of the routine, the genetic algorithm “Non‐Dominated Sorting Genetic Algorithm II (NSGA‐II)” is used to generate an initial approximation of the Pareto front that covers a wide variety of possible solutions, that is, optimal trade‐offs between the conflicting objectives. Subsequently, to ensure convergence, the trust region optimizer “Constrained Multiobjective Problem Optimizer with Model Information to Save Evaluations (CoMPrOMISE)” is used, which is initialized with individuals selected from the Pareto set generated by the genetic algorithm.

Effective nonmonotone trust region method based on a simple cubic model for unconstrained optimization problems

Effective nonmonotone trust region method based on a simple cubic model for unconstrained optimization problems

A Quasi-Newton Subspace Trust Region Algorithm for Nonmonotone Variational Inequalities in Adversarial Learning over Box Constraints

The first-order optimality condition of convexly constrained nonconvex nonconcave min-max optimization problems with box constraints formulates a nonmonotone variational inequality (VI), which is equivalent to a system of nonsmooth equations. In this paper, we propose a quasi-Newton subspace trust region (QNSTR) algorithm for the least squares problems defined by the smoothing approximation of nonsmooth equations. Based on the structure of the nonmonotone VI, we use an adaptive quasi-Newton formula to approximate the Hessian matrix and solve a low-dimensional strongly convex quadratic program with ellipse constraints in a subspace at each step of the QNSTR algorithm efficiently. We prove the global convergence of the QNSTR algorithm to an ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon $$\\end{document}-first-order stationary point of the min-max optimization problem. Moreover, we present numerical results based on the QNSTR algorithm with different subspaces for a mixed generative adversarial networks in eye image segmentation using real data to show the efficiency and effectiveness of the QNSTR algorithm for solving large-scale min-max optimization problems.

Internal Ties and Stock Price Crash Risk: Evidence from Chinese Listed Firms

Drawing on information advantage and executive entrenchment perspectives, this study examines the impact of internal ties between independent directors and non‐CEO executives (hereafter, internal ties) on stock price crashes. Utilizing a dataset covering Chinese listed firms spanning 2005 to 2021, we find that internal ties alleviate information asymmetry between the board and management, reducing future stock price crash risk. This supports the information advantage hypothesis. Further analysis reveals the effect of internal ties on stock price crash risk is more evident in high social trust regions and among non‐state‐owned enterprises (non‐SOEs). Mechanism tests demonstrate that financial opacity and financial reporting conservatism are economic mechanisms through which internal ties affect stock price crashes. Our research sheds new light regarding the significance of internal ties in corporate governance and enriches the literature on internal governance.

A New Hybrid Descent Algorithm for Large-Scale Nonconvex Optimization and Application to Some Image Restoration Problems

Conjugate gradient methods are widely used and attractive for large-scale unconstrained smooth optimization problems, with simple computation, low memory requirements, and interesting theoretical information on the features of curvature. Based on the strongly convergent property of the Dai–Yuan method and attractive numerical performance of the Hestenes–Stiefel method, a new hybrid descent conjugate gradient method is proposed in this paper. The proposed method satisfies the sufficient descent property independent of the accuracy of the line search strategies. Under the standard conditions, the trust region property and the global convergence are established, respectively. Numerical results of 61 problems with 9 large-scale dimensions and 46 ill-conditioned matrix problems reveal that the proposed method is more effective, robust, and reliable than the other methods. Additionally, the hybrid method also demonstrates reliable results for some image restoration problems.

Research on Supply Chain Optimization and Management Based on Deep Reinforcement Learning

This research introduces a groundbreaking approach to supply chain optimization and management, termed as Deep Reinforcement Learning based Supply Chain Optimization and Management (DRL-SCOM). At the core of this approach is the utilization of advancements in Deep Reinforcement Learning (DRL), specifically through the integration of Randomized Ensembled Double Q-learning (REDQ) and Trust Region Policy Optimization (TRPO). DRL-SCOM is designed to effectively tackle the inherent complexities and dynamic challenges that are characteristic of supply chain management. One of the key strengths of DRL-SCOM lies in its use of REDQ, which plays a crucial role in mitigating the overestimation bias commonly associated with traditional Q-learning methods. This results in more accurate value estimation and policy improvement, a critical factor in the effective management of supply chains. Additionally, the integration of TRPO into the framework brings the advantage of safe and stable policy updates. Such stability is vital for maintaining the robustness required in the fluctuating environment of supply chain operations. The combination of REDQ and TRPO in DRL-SCOM creates a powerful synergy. REDQ’s ensembled learning approach, when fused with TRPO’s trust-region method, enables the framework to efficiently navigate the complex and high-dimensional decision space typical of supply chains. This allows for real-time optimization of decisions while staying within operational constraints. The DRL-SCOM methodology shows significant potential in addressing various aspects of supply chain management, from demand forecasting and inventory management to logistics, adeptly handling the nonlinearities and uncertainties that are prevalent in these areas. Thus, the DRL-SCOM framework emerges as an innovative solution, pushing the frontiers of traditional supply chain management. It paves the way for a more agile, responsive, and intelligent system, equipped to adapt to changing market demands and operational challenges. This approach represents a significant stride towards transforming supply chain management into a more advanced, data-driven, and adaptive field.

Innovative energy solutions: Evaluating reinforcement learning algorithms for battery storage optimization in residential settings

The implementation of BESS (battery energy storage systems) and the efficient optimization of their scheduling are crucial research challenges in effectively managing the intermittency and volatility of solar-PV (photovoltaic) systems. Nevertheless, an examination of the existing body of knowledge uncovers notable deficiencies in the ideal arrangement of energy systems' timetables. Most models primarily concentrate on a single aim, whereas only a few tackle the intricacies of multi-objective scenarios. This study examines homes connected to the power grid equipped with a BESS and a solar PV system. It leverages four distinct reinforcement learning (RL) algorithms, selected for their unique training methodologies, to develop effective scheduling models. The findings demonstrate that the RL model using Trust Region Policy Optimization (TRPO) effectively manages the BESS and PV system despite real-world uncertainties. This case study confirms the suitability and effectiveness of this approach. The TRPO-based RL framework surpasses previous models in decision-making by choosing the most optimal BESS scheduling strategies. The TRPO model exhibited the highest mean self-sufficiency rates compared to the A3C (Asynchronous Advantage Actor-Critic), DDPG (Deep Deterministic Policy Gradient), and TAC (Twin Actor Cretic) models, surpassing them by ∼ 3 %, 0.72 %, and 3.5 %, correspondingly. This results in enhanced autonomy and economic benefits by adapting to dynamic real-world conditions. Consequently, our approach was strategically designed to deliver an optimized outcome. This framework is primarily intended for seamless integration into an automated energy plant environment, facilitating regular electricity trading among multiple buildings. Backed by initiatives like the Renewable Energy Certificate weight, this technology is expected to play a crucial role in maintaining a balance between power generation and consumption. The MILP (Mixed Integer Linear Programming) architecture achieved a self-sufficiency rate of 29.12 %, surpassing the rates of A3C, TRPO, DDPG, and TAC by 2.48 %, 0.64 %, 2 %, and 3.04 %, correspondingly.

A Modified Wei-Yao-Liu Stochastic Conjugate Gradient Algorithm in Machine Learning

Abstract The Wei-Yao-Liu (WYL) Conjugate Gradient (CG) algorithm exhibits favourable attributes, notably sufficient descent and trust domain characteristics, in the context of solving unconstrained optimization problems. The exploration and enhancement of computational methodologies for stochastic optimization problems have garnered significant attention. In this study, our objective is to improve the Wei-Yao-Liu (WYL) CG algorithm and introduce an effective optimization method tailored for solving stochastic optimization problems. We will present a comprehensive framework for analysing the convergence of this algorithm and, under suitable conditions, establish its sufficient descent properties, trust region features, and global convergence of stationary points. We will also give an improved CG algorithm to calculate a framework for variance reduction. Additionally, we will conduct experimental comparisons to showcase the competitiveness of our proposed algorithm.

A Modified Three-terms CG Method with the MWWP Line Search and its Application to Image Restoration

Abstract In this article, an innovative method, which integrates the optimized three-term Polak–Ribière–Polyak (PRP) conjugate gradient (CG) method with the improved WWP line search rule, is presented and applied in the field of image restoration. The proposed search direction exhibits sufficient descent and trust region characteristics, maintaining its effectiveness regardless of the specific line search rule employed. We established the global convergence of the presented algorithm and eliminated the dependence on the Lipschitz continuity assumption. The numerical comparisons with the PRP CG method revealed the superior performance of the designed algorithm in the field of image restoration. This research outcome provides strong support for further advancements in the field of image recovery.

Adaptive reduced basis trust region methods for parameter identification problems

In this contribution, we are concerned with model order reduction in the context of iterative regularization methods for the solution of inverse problems arising from parameter identification in elliptic partial differential equations. Such methods typically require a large number of forward solutions, which makes the use of the reduced basis method attractive to reduce computational complexity. However, the considered inverse problems are typically ill-posed due to their infinite-dimensional parameter space. Moreover, the infinite-dimensional parameter space makes it impossible to build and certify classical reduced-order models efficiently in a so-called “offline phase”. We thus propose a new algorithm that adaptively builds a reduced parameter space in the online phase. The enrichment of the reduced parameter space is naturally inherited from the Tikhonov regularization within an iteratively regularized Gauß-Newton method. Finally, the adaptive parameter space reduction is combined with a certified reduced basis state space reduction within an adaptive error-aware trust region framework. Numerical experiments are presented to show the efficiency of the combined parameter and state space reduction for inverse parameter identification problems with distributed reaction or diffusion coefficients.

A Pn-wave spectral inversion technique based on trust region reflective algorithm

This paper suggests utilizing the trust region reflective (TRR) algorithm to address the inverse problem related to seismic spectrum analysis of Pn waves. By applying this approach, it becomes feasible to simultaneously deduce the seismic moment, corner frequency, tomographic model of Pn-wave attenuation, and site responses while incorporating appropriate constraints based on prior knowledge to ensure solution accuracy. The efficacy of this method has been validated using synthetic data. Specifically, the recorded Pn waves from four underground explosions in North Korea were employed to evaluate the performance of the proposed technique. The derived seismic moment and corner frequency for these events were found to align with the characteristics of the seismic data, earthquake magnitude calculations, and empirical data. The resulting tomographic model of Pn-wave attenuation revealed a spatial distribution of high and low attenuation, indicating significant lithospheric heterogeneity in northeastern China. Areas with low Q0 and low η, such as the Xialiaohe Basin and southwestern Changbai Mountain, suggest a high-temperature environment in the upper mantle cap layer or the presence of molten substances. Conversely, regions with high Q0 and high η, like the northern Changbai Mountain and the vicinity of the eastern Tanlu Fault Zone, characterized by high Pn-wave velocity and thick crust, indicate minimal modification or destruction in the lithosphere. Furthermore, site responses were determined for 75 seismic stations in northeastern China, with their characteristics preliminarily analyzed and interpreted in conjunction with geological context. The iterative process based on the TRR algorithm for Pn-wave spectral inversion proposed in this study demonstrates robust convergence and enhances the fitting accuracy of the observed spectrum. The inversion outcomes from this spectral technique yielded synthetic Pn-wave spectra that closely matched the observed spectra of the four underground explosions in North Korea across various frequency bands for over 90 % of the stations.

RBF-ARX model-based trust region nonlinear model predictive control and its application on magnetic levitation ball system

RBF-ARX model-based trust region nonlinear model predictive control and its application on magnetic levitation ball system

Riemannian Trust Region Methods for $$\hbox {SC}^1$$ Minimization

Riemannian Trust Region Methods for $$\hbox {SC}^1$$ Minimization

Homotopy trust-region method for phase-field approximations in perimeter-regularized binary optimal control

We consider optimal control problems that have binary-valued control input functions and a perimeter regularization. We develop and analyze a trust-region algorithm that solves a sequence of subproblems in which the regularization term and the binarity constraint are relaxed by a non-convex energy functional. We show how the parameter that controls the distinctiveness of the resulting phase field can be coupled to the trust-region radius updates and be driven to zero over the course of the iterations in order to obtain convergence to points that satisfy a first-order optimality condition of the limit problem under suitable regularity assumptions. Finally, we highlight and discuss the assumptions and restrictions of our approach and provide the first computational results for a motivating application in the field of control of acoustic waves in dissipative media.

Fast convergence to non-isolated minima: four equivalent conditions for $${\textrm{C}^{2}}$$ functions

AbstractOptimization algorithms can see their local convergence rates deteriorate when the Hessian at the optimum is singular. These singularities are inescapable when the optima are non-isolated. Yet, under the right circumstances, several algorithms preserve their favorable rates even when optima form a continuum (e.g., due to over-parameterization). This has been explained under various structural assumptions, including the Polyak–Łojasiewicz condition, Quadratic Growth and the Error Bound. We show that, for cost functions which are twice continuously differentiable ($$\textrm{C}^2$$ C 2 ), those three (local) properties are equivalent. Moreover, we show they are equivalent to the Morse–Bott property, that is, local minima form differentiable submanifolds, and the Hessian of the cost function is positive definite along its normal directions. We leverage this insight to improve local convergence guarantees for safe-guarded Newton-type methods under any (hence all) of the above assumptions. First, for adaptive cubic regularization, we secure quadratic convergence even with inexact subproblem solvers. Second, for trust-region methods, we argue capture can fail with an exact subproblem solver, then proceed to show linear convergence with an inexact one (Cauchy steps).