Trust Region Research Articles

The trust region filter strategy: Survey of a rigorous approach for optimization with surrogate models

The trust region filter strategy: Survey of a rigorous approach for optimization with surrogate models

Adaptive Pseudospectral Successive Convex Optimization for Six-Degree-of-Freedom Powered Descent Guidance

Guidance for six-degrees-of-freedom powered descent is more challenging due to its stronger nonlinearity compared to three-degrees-of-freedom. The standard convex programming algorithm has been difficult to effectively address this problem. To enhance the performance of successive convex programming in terms of both optimality and accuracy, an adaptive pseudospectral successive convex optimization algorithm is proposed in this paper. First, it transforms the nonlinear optimal control problem into a convex subproblem by integrating global pseudospectral discretization with local linearization. Second, a parameter-adaptive successive convexification algorithm is proposed, which adaptively adjusts the trust region size based on the update rate of the optimal trajectory. Last, the global error and local error are accurately calculated based on the pseudospectral method. To tackle the issue of excessively large local errors caused by nonlinearity, an adaptive grid method is proposed to refine the mesh grid. Simulation results demonstrate the efficacy of the proposed pseudospectral convex optimization method and adaptive mesh grid method in reducing local errors and improving solution accuracy. Furthermore, the proposed parameter-adaptive successive convex optimization algorithm exhibits adaptability and optimality across different initial conditions, while also improving solution accuracy.

Galvanic distortion decomposition of magnetotelluric impedance tensors in 1-D electrical anisotropic media

SUMMARY The electromagnetic (EM) local distortion of the transfer function due to shallow small-scale inhomogeneities hinders the accurate interpretation of magnetotelluric (MT) data. Under the assumption that regional subsurface structures are electrically isotropic, decomposition techniques of the MT impedance tensor that focus on the galvanic distortion of the electric field have been well developed. In this paper, we present a decomposition method of MT impedance tensors over a regional 1-D conductivity anisotropic Earth, in which the galvanic distortion of both the electric and the associated magnetic fields are taken into account. An eigenparameter analysis is introduced to evaluate the intrinsic indeterminacy of magnetic distortion parameters. Regional anisotropic responses and EM distortion parameters are resolved by using a modified BFGS (Broyden–Fletcher–Goldfarb–Shanno) quasi-Newton algorithm combined with phase tensor analysis and the trust region method. In the presence of near-surface anisotropic inhomogeneities, synthetic 2-D data show an accentuated magnetic galvanic effect in the response tensors especially in the diagonal components probably due to the infinite extension in the strike direction. However, the magnetic galvanic distortion is not significant in synthetic 3-D models. The decomposition scheme is also applied to the analysis of the BC87 data set collected in southeastern British Columbia to investigate both the electric and magnetic field galvanic distortion.

Riemannian trust-region methods for strict saddle functions with complexity guarantees

Riemannian trust-region methods for strict saddle functions with complexity guarantees

Enhancing Collaboration in Heterogeneous Multiagent Systems Through Communication Complementary Graph.

Heterogeneous multiagent systems are characterized by diverse task distributions, which are prevalent in practical scenarios, such as distributed decision making and robotic collaboration. A significant challenge in these systems is the constraint of limited observations, where each agent has access only to partial information. Many studies facilitate information exchange by employing shared parameters among agents. However, this approach is generally more effective for homogeneous systems where agents have similar observation or action spaces. In heterogeneous systems, indiscriminate parameter sharing can significantly increase the exploration cost required for effective adaptation. To address this challenge, we propose a novel communication complementary graph model (CCGM) for enhancing collaboration in heterogeneous multiagent systems. Our approach builds upon the training framework of heterogeneous agent reinforcement learning (HARL) with trust region learning and nonparameter sharing. This model utilizes advantage function decomposition and sequential updates to promote policy convergence. Within this framework, we introduce a novel communication method inspired by signaling games, where agents acting as receivers, process messages from other agents alongside their own observations. CCGM aligns the messages with observations in a graph-based communication module, which establishes communication relationships and supplements observational information. Subsequently, agents generate self-interested information, which they then share with others as senders. We evaluate our algorithm across various environments, including multiagent particle environments (MPE) and multiagent MuJoCo (MAMuJoCo) robot experiments. The results demonstrate the effectiveness of CCGM in enhancing HARL-based algorithms.

Design and research of a monitoring and environmental testing analysis system for substation status

Abstract By testing and analyzing the real substation environment, and analyzing and fitting on-site data, a system that simulates the operating environment of the real substation is designed, and the goal of replicating a typical on-site electricity environment is achieved. Testing and analysis are conducted on the selected substation area, and light and heavy load noise is collected for spectrum analysis and measurement point attenuation analysis. The LMF (Late Multimodal Fusion) algorithm is used and test data are fitted based on the trust region theory. Conducting noise testing and attenuation analysis in the substation area has laid the foundation for research on substation status monitoring and environmental monitoring.

An Improved Non-Monotonic Adaptive Trust Region Algorithm for Unconstrained Optimization

The trust region method is an effective method for solving unconstrained optimization problems. Incorrectly updating the rules of the trust region radius will increase the number of iterations and affect the calculation efficiency. In order to obtain an effective radius for the trust region, an adaptive radius updating criterion is proposed based on the gradient of the current iteration point and the eigenvalue of the Hessian matrix which avoids calculating the inverse of the Hessian matrix during radius updating. This approach reduces the computation time and enhances the algorithm’s performance. On this basis, we apply adaptive radius and non-monotonic techniques to the trust region algorithm and propose an improved non-monotonic adaptive trust region algorithm. Under proper assumptions, the convergence of the algorithm is analyzed. Numerical experiments confirm that the suggested algorithm is effective.

Convergence Rate of Greedy SR1 With Trust Region Method

Convergence Rate of Greedy SR1 With Trust Region Method

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

The 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.

A two-step relaxed-inertial derivative-free projection based algorithm for solving standard nonlinear pseudo-monotone equations and logistic regression problems

This paper explores a two-step inertial derivative-free projection method with a relaxation factor γ∈(0,2) for solving nonlinear pseudo-monotone equations. Unlike existing inertial algorithms for the system of nonlinear pseudo-monotone equations, the inertial step of our method involves the current iteration point and the previous two iteration points. In particular, one of the inertial parameters is nonpositive. In the proposed algorithm, the search direction possesses not only the sufficient descent property but also the trust region property, independent of the line search technique. Moreover, we also establish the global convergence and the convergence rate of the algorithm without the Lipschitz continuity of the underlying mapping. Finally, our method provides competitive results on standard nonlinear monotone and pseudo-monotone equations and logistic regression problems compared with two inertial algorithms existing in the literature.

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.