Trust Region Research Articles

A constrained optimisation framework for parameter identification of the SIRD model.

We consider a numerical framework tailored to identifying optimal parameters in the context of modelling disease propagation. Our focus is on understanding the behaviour of optimisation algorithms for such problems, where the dynamics are described by a system of ordinary differential equations associated with the epidemiological SIRD model. Applying an optimise-then-discretise approach, we examine properties of the solution operator and determine existence of optimal parameters for the problem considered. Further, first-order optimality conditions are derived, the solution of which provides a certificate of goodness of fit, which is not always guaranteed with parameter tuning techniques. We then propose strategies for the numerical solution of such problems, based on projected gradient descent, Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), nonmonotone Accelerated Proximal Gradient (nmAPG), and limited memory BFGS trust region approaches. We carry out a thorough computational study for a range of problems of interest, determining the relative performance of these numerical methods. Our results provide insights into the effectiveness of these strategies, contributing to ongoing research into optimising parameters for accurate and reliable disease spread modelling. Moreover, our approach paves the way for calibration of more intricate compartmental models.

Joint Precoding and Phase Shift Design for RIS-Aided Cell-Free Massive MIMO With Heterogeneous-Agent Trust Region Policy

Joint Precoding and Phase Shift Design for RIS-Aided Cell-Free Massive MIMO With Heterogeneous-Agent Trust Region Policy

The design‐manufacturing‐evaluation integration of a bionic stealth metastructure inspired by the weevils back shell structure

AbstractWith the advancement of technology, the demand for high‐performance stealth materials with complex structures has increased significantly. This study explores the integration of design, manufacturing, and evaluation of stealth structures using fused deposition modeling (FDM) combined with advanced absorbing materials. Focusing on nylon‐based filaments optimized for broadband absorption, the research is inspired by the microstructure of the weaver ant's back shell to create a thin‐layer, wideband absorbing structure with wide‐angle response, employing the trust region algorithm. This integration of high dielectric loss materials, bionic design, and FDM technology enhances manufacturing efficiency and reduces the structure's thickness. The resulting structure achieves broadband absorption from 3.56 to 40 GHz, excellent angular adaptability, and mechanical robustness. Compared to gradient cell structures, it reduces thickness by 33% and extends the absorption frequency range by 5%. This approach offers a lightweight, high‐performance solution for next‐generation stealth applications.Highlights Biomimetic inspired design‐manufacturing‐evaluation integration. Trust domain algorithm optimization. Improve absorption by combining the macro structure and micro materials. Additive manufacturing cross‐enabled functional material design.

Comparative Analysis of Deep Reinforcement Learning Algorithms for Hover-to-Cruise Transition Maneuvers of a Tilt-Rotor Unmanned Aerial Vehicle

Work on trajectory optimization is evolving rapidly due to the introduction of Artificial-Intelligence (AI)-based algorithms. Small UAVs are expected to execute versatile maneuvers in unknown environments. Prior studies on these UAVs have focused on conventional controller design, modeling, and performance, which have posed various challenges. However, a less explored area is the usage of reinforcement-learning algorithms for performing agile maneuvers like transition from hover to cruise. This paper introduces a unified framework for the development and optimization of a tilt-rotor tricopter UAV capable of performing Vertical Takeoff and Landing (VTOL) and efficient hover-to-cruise transitions. The UAV is equipped with a reinforcement-learning-based control system, specifically utilizing algorithms such as Deep Deterministic Policy Gradient (DDPG), Trust Region Policy Optimization (TRPO), and Proximal Policy Optimization (PPO). Through extensive simulations, the study identifies PPO as the most robust algorithm, achieving superior performance in terms of stability and convergence compared with DDPG and TRPO. The findings demonstrate the efficacy of DRL in leveraging the unique dynamics of tilt-rotor UAVs and show a significant improvement in maneuvering precision and control adaptability. This study demonstrates the potential of reinforcement-learning algorithms in advancing autonomous UAV operations by bridging the gap between dynamic modeling and intelligent control strategies, underscoring the practical benefits of DRL in aerial robotics.

Issues on a 2–Dimensional Quadratic Sub–Problem and Its Applications in Nonlinear Programming: Trust–Region Methods (TRMs) and Linesearch Based Methods (LBMs)

This paper analyses the solution of a specific quadratic sub-problem, along with its possible applications, within both constrained and unconstrained Nonlinear Programming frameworks. We give evidence that this sub–problem may appear in a number of Linesearch Based Methods (LBM) schemes, and to some extent it reveals a close analogy with the solution of trust–region sub–problems. Namely, we refer to a two-dimensional structured quadratic problem, where five linear inequality constraints are included. Finally, we detail how to compute an exact global solution of our two-dimensional quadratic sub-problem, exploiting first order Karush-Khun-Tucker (KKT) conditions.

A conic regularized Barzilai–Borwein trust region method for large scale unconstrained optimization

A conic regularized Barzilai–Borwein trust region method for large scale unconstrained optimization

Rank-one approximation of a higher-order tensor by a Riemannian trust-region method

Rank-one approximation of a higher-order tensor by a Riemannian trust-region method

Random uncertain motor parameters identification combining fourth-order moment and trust region

In random uncertain motor parameter identification field, there is low identification efficiency and ill-conditioned data coming from the second iteration involved in the uncertainty propagation and surrogate model between the motor parameters and the performance response. In this paper, the fourth-order moment method and trust region model management technology are combined to reduce the dependence of the surrogate model accuracy and improve the computational efficiency. In the framework, the inner layer calculates the cumulative probability under different motor performance response thresholds based on the fourth-order moment method, and obtain the probability density function of the calculated motor performance response. The outer layer transforms the random uncertain motor parameters identification into a deterministic optimization problem by minimizing the probability distribution between the calculated and the measured motor performance response. In the outer layer optimization, the trust region model management technology is used to divide the search interval of the entire parameter to be identified into a series of trust regions, construct a surrogate model on the trust region to calculate the motor performance response, and continuously update the trust region by comparing the response residuals between the calculated and measured motor performance response, so that the motor parameters to be identified continue to approach the interval where true values are located. At the same time, the genetic intelligent technology is introduced to further reduce the calculation cost. Finally, the probability distribution of random uncertain motor parameters is obtained according to the identified mean, standard deviation, skewness and kurtosis coefficients. The numerical results in the example verify that the random uncertain motor parameter identification can be effectively achieved by the proposed method.

Improved Algorithms Based on Trust Region Framework for Solving Unconstrained Derivative Free Optimization Problems

This paper is devoted to developing new derivative-free optimization (DFO) methods for solving optimization problems where derivative information is not available or cannot be calculated numerically. To overcome the computational difficulties arising from time-consuming estimations of the objective function, we propose two algorithms. One algorithm is a variant of the surrogate model-based DFO algorithm under the trust region method, where the surrogate model is formulated through sparse low-rank interpolation and quadratic polynomial interpolation. This algorithm serves as a comparative baseline. The second algorithm leverages the characteristics of the sparse regression model, which can handle sparsity and noise issues, to construct the surrogate model. The coefficients of the sparse surrogate model are then estimated using the alternating direction method of multipliers and refined through a correction strategy based on the R-square. Finally, numerical results, evaluated in terms of performance and data profiles, demonstrate the effectiveness and competitiveness of the proposed algorithms.

An inertial conjugate gradient projection method for large-scale nonlinear equations and its application in the image restoration problems

Based on the acceleration effect of the inertial extrapolation technique on the convergence of iterative sequences, the number of algorithms incorporating this technique has gradually increased in recent years. Currently, there is a relative paucity of studies focusing on the Polak-Ribière-Polyak (PRP) conjugate gradient algorithm that integrate the inertial extrapolation technique. In this article, we introduce an inertial three-term PRP conjugate gradient projection method by incorporating an inertial extrapolation step into the three-term PRP algorithm, where the search direction exhibits sufficient descent and trust region characteristics. The search rule employs a derivative-free technique. Under suitable hypotheses, the proposed algorithm demonstrates global convergence. Numerical results indicate the superiority and competitiveness of this innovative method. Furthermore, its effectiveness in addressing image restoration problems underscores the practicality of this algorithm.

Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms

The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. We numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue. Funding: This material is based upon work supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers and the Office of Advanced Scientific Computing Research, Accelerated Research for Quantum Computing program under contract number DE-AC02-06CH11357. Y. Ha and S. Shashaani also gratefully acknowledge the U.S. National Science Foundation Division of Civil, Mechanical and Manufacturing Innovation Grant CMMI-2226347 and the U.S. Office of Naval Research [Grant N000142412398]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0575 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0575 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Secure model predictive static programming with initial value generator for online computational guidance of near-space vehicles

For online trajectory programming of near-space vehicles with limited computation resources, conventional model predictive static programming approaches have two main challenges. Firstly, an inadequate initial control guess can lead to trajectory divergence or slow convergence, resulting in mission failure. Secondly, Euler discretization is a small-step local algorithm by point-to-point recursion. To ensure high precision solution, more discretization points are required, leading to low computation efficiency and accuracy; meanwhile conventional methods cannot guarantee that the problems are solved within the constraints and feasible domains, potentially affecting the solution stability. To solve the first problem, a variable coefficient near-optimal initial value generator is developed to provide an initial control guess that approximates the optimal trajectory, preventing divergence in subsequent iterations. To address the second problem, the trust-region constrained model predictive static programming is proposed with flipped-Radau pseudospectrum. This method reduces the number of discretization points and optimizes the performance index directly, thereby enhancing efficiency; meanwhile the trust region improves accuracy and ensures the updated trajectory remains close to the reference trajectory. Finally, the combination of above approaches enhances the calculating efficiency and precision significantly for online trajectory programming. Applied to a near-space vehicle, the proposed method reduces optimization time by 25 % for rapid and high-precision solutions, and improves terminal position accuracy from 43 m to 1 m with flipped-Radau pseudospectrum.

Improving generalization performance of adaptive gradient method via bounded step sizes

While adaptive gradient methods such as Adam have been widely used in the training of deep neural networks, a recent study has provided a synthetic function that shows the non-convergence problem of Adam. This issue stems from the existence of extreme gradients and the mismatch between the first and second moments. Several adaptive optimizers have been continuously developed. However, designing a fast optimizer with excellent generalization capability is still challenging. We propose an adaptive method with bounded step sizes, named AdaBS, which removes the extreme step sizes and ensures that it appropriately adjusts adaptive step sizes to mitigate the over-adaptation of step sizes in Adam. In particular, AdaBS effectively clips step sizes that are too large or too small by using two static bounds with a predetermined boundary to control updates. When determining the step size, static bound clipping will be used if the preconditioner is outside the modest boundary, and vanilla Adam will be used if the preconditioner is inside the boundary. AdaBS establishes a trust region around the basic step size and obtains benefits of both Adam and SGD, i.e. fast convergence and better generalization. Finally, we conduct extensive experiments on a variety of practical tasks with benchmark datasets, including image classification and modeling language tasks. Empirical results demonstrate AdaBS’s promising performance with remarkably fast convergence, superior generalization, and robustness.

Optimal Design of Rectangular Tank Walls With Ribs Using Numerical Models and Global Optimization

This paper addresses the optimization of the cross-section in rectangular above-ground tank walls, incorporating vertical ribs and an optional top ring. The objective is to minimize the volume of concrete used, while maintaining key performance criteria such as keeping the maximum tensile stress below the material’s allowable limit and minimizing deflections. The analysis is performed using the finite element method (FEM), with the optimization handled through a local gradient-based algorithm (trust region method), supported by a multistart technique to navigate the complexity of the design space and avoid suboptimal solutions. The results demonstrate that this approach effectively reduces concrete consumption without exceeding the tensile stress limits or causing excessive deflection, offering more efficient and cost-effective designs for rectangular tanks used in water storage applications. This method provides valuable insights into the balance between material usage and performance constraints, contributing to sustainable engineering practices.

An inertial hybrid DFPM-based algorithm for constrained nonlinear equations with applications

The derivative-free projection method (DFPM) is an effective and classic approach for solving the system of nonlinear monotone equations with convex constraints, but the global convergence or convergence rate of the DFPM is typically analyzed under the Lipschitz continuity. This observation motivates us to propose an inertial hybrid DFPM-based algorithm, which incorporates a modified conjugate parameter utilizing a hybridized technique, to weaken the convergence assumption. By integrating an improved inertial extrapolation step and the restart procedure into the search direction, the resulting direction satisfies the sufficient descent and trust region properties, which independent of line search choices. Under weaker conditions, we establish the global convergence and Q-linear convergence rate of the proposed algorithm. To the best of our knowledge, this is the first analysis of the Q-linear convergence rate under the condition that the mapping is locally Lipschitz continuous. Finally, by applying the Bayesian hyperparameter optimization technique, a series of numerical experiment results demonstrate that the new algorithm has advantages in solving nonlinear monotone equation systems with convex constraints and handling compressed sensing problems.

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

Recent developments in efficient, large-scale nonlinear optimization strategies have had significants impact on the design and operation of engineering systems with equation-oriented (EO) models. On the other hand, rigorous first-principle procedural (i.e., black-box ’truth’) models may be difficult to incorporate directly within this optimization framework. Instead, black-box models are often substituted by lower fidelity surrogate models that may compromise the optimal solution. To overcome these challenges, Trust Region Filter (TRF) methods have been developed, which combine surrogate models optimization with intermittent sampling of truth models. The TRF approach combines efficient solution strategies with minimal recourse to truth models, and leads to guaranteed convergence to the truth model optimum. This survey paper provides a perspective on the conceptual development and evolution of the TRF method along with a review of applications that demonstrate the effectiveness of the TRF approach. In particular, three cases studies are presented on flowsheet optimization with embedded CFD models for advanced power plants and CO2 capture processes, as well as synthesis of heat exchanger networks with detailed finite-element equipment models.

Aerodynamic robustness optimization of aeroengine fan performance based on an interpretable dynamic machine learning method

Aeroengines and gas turbines are susceptible to uncertainties during manufacturing and operation, leading to reduced efficiency and dispersed performance. Current engine design system often produces deterministic performance databases that cannot be effectively used to guide the uncertainty analysis and robust design process of turbomachinery. This paper proposes an interpretable dynamic machine learning method for sensitivity analysis and robust optimization of turbomachinery blades. A dynamic extreme gradient boosting (XGBoost) is trained to predict fan aerodynamic performance, and the SHapley additional explanation (SHAP) method is introduced to explain regression model behavior and identify the impact of uncertain variables. On this basis, the Lipschitz-based trust region (MAXLIPO-TR) optimization algorithm is used to obtain the optimal configuration with the best robustness performance. Finally, the method is applied to data mining for design guidelines of robustness performance enhancement of an aeroengine fan. The results show that maximum camber and tangential stacking have major effects on fan performance dispersion. The standard deviation of the isentropic efficiency, pressure ratio and mass flow rate of the optimized configuration are reduced by 42.4%, 35.6% and 22.7% respectively at design conditions. The proposed data mining method has scientific significance and industrial application value in the robust design of advanced turbomachinery.

The pupil outdoes the master: Imperfect demonstration-assisted trust region jamming policy optimization against frequency-hopping spread spectrum

Jamming decision-making is a pivotal component of modern electromagnetic warfare, wherein recent years have witnessed the extensive application of deep reinforcement learning techniques to enhance the autonomy and intelligence of wireless communication jamming decisions. However, existing researches heavily rely on manually designed customized jamming reward functions, leading to significant consumption of human and computational resources. To this end, under the premise of obviating designing task-customized reward functions, we propose a jamming policy optimization method that learns from imperfect demonstrations to effectively address the complex and high-dimensional jamming resource allocation problem against frequency hopping spread spectrum (FHSS) communication systems. To achieve this, a policy network is meticulously architected to consecutively ascertain jamming schemes for each jamming node, facilitating the construction of the dynamic transition within the Markov decision process. Subsequently, anchored in the dual-trust region concept, we design policy improvement and policy adversarial imitation phases. During the policy improvement phase, the trust region policy optimization method is utilized to refine the policy, while the policy adversarial imitation phase employs adversarial training to guide policy exploration using information embedded in demonstrations. Extensive simulation results indicate that our proposed method can approximate the optimal jamming performance trained under customized reward functions, even with rough binary reward settings, and also significantly surpass demonstration performance.

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