Interior Point Method Research Articles

Non-Destructive Damage Evaluation Based on Static Response for Beam-like Structures Considering Shear Deformation

Shear deformation plays an important role in certain structures, and neglecting shear deformation can affect the accuracy of structural response. This paper proposes a non-destructive damage evaluation method that considers shear deformation, based on static response, for identifying corrosion in beam-like structures. The influence of shear deformation on nodal displacement for simply supported beams with different cross-sections was analyzed. The results indicate that even small errors yield inaccurate identification results when neglecting shear deformation. To solve this problem, analytical displacements of the structure were determined based on the Timoshenko beam theory, and the objective function was established. Additionally, the damage identification results were obtained by minimizing the objective function using the interior point method. Several progressively complex examples were used to demonstrate the effectiveness of the proposed method in identifying damage in beam-like structures.

Foreign bodies inside us - Trends and knowledge regarding long-acting reversible contraceptives (LARCs) use, factors influencing of contraceptives choice-making process, and the dual-method use among Polish college-aged women

Introduction: The choice-making process of the contraceptive method seems complex and influenced by many factors. Long-acting reversible contraceptives require mechanical interference with the woman's body. For some, it will be an insurmountable barrier whilst for others a chance to enjoy a successful sex life without fear of pregnancy. Recognizing the factors influencing their use will allow us to identify target groups, increase awareness, and spread knowledge about them.
 Purpose: This study aimed to assess contraceptive use trends and knowledge, focusing on long-acting reversible contraceptives (LARCs) and vaginal rings, also to identify predictors associated with their use and analyze the decision-making process for dual-method use (hormonal plus barrier method) among female college students in Poland.
 Materials and methods: A self-administered questionnaire including 44 questions in the form of a web-based survey distributed among peers in social media platforms and forums.
 Results: In the survey a total of 700 female students aged 19±25 took part. All the questions about LARC and vaginal rings were answered correctly by only 19 participants (2.71%). The most knowledgeable were medical students (p<0.0001). Out of 55 LARC and vaginal ring users (7.86%), 47 female students (76.4%,) stated the improvement of their life. Of the methods interfering with the body, the study group most frequently chose the vaginal ring (38.1%) and least frequently the hormone injection (0.1%). 
 Conclusions: Participants’ knowledge of LARC methods and vaginal rings is insufficient and its main influencing factors are faculty type and frequency of intercourse. LARC and vaginal disc are not the first contraception choice. Fear of pregnancy is the most common factor for dual method use.

Complexity analysis of interior-point methods for second-order stationary points of nonlinear semidefinite optimization problems

Complexity analysis of interior-point methods for second-order stationary points of nonlinear semidefinite optimization problems

A Method for tackling multiplicity in dynamic flux balance models by an ellipsoidal reflection operation

Dynamic Flux Balance Models (DFBM) can describe the evolution of metabolites’ concentrations with time by solving a linear programming (LP) problem at each time interval. However, since multiple solutions of the LP commonly exist, different trajectories can be obtained. An interior-point based method (weighted primal–dual method) proposed in a previous study that picks a specific solution from multiple solutions of LP is computationally expensive for a large metabolic network. In this research, we propose an alternative computationally efficient method based on an ellipsoidal reflection mathematical operation. The method is applied to different examples to demonstrate the algorithm and its computational efficiency and then for modeling the fermentation of B. pertussis resulting in excellent computational performance and accurate fitting of experimental dynamic data.

RED WoLF hybrid energy storage system: Algorithm case study and green competition between storage heaters and heat pump

Green house gases reduction is critical in current climate emergency and was declared as major target by United Nations. This manuscript proposes the progressive adaptive recursive multi threshold control strategy for hybrid energy storage system that combines thermal storage reservoirs, heat pumps, storage heaters, photovoltaic array and a battery. The newest control strategy is tested in numerical experiment against primal dual simplex optimisation method as benchmark and previous iterations of RED WoLF threshold approaches. The proposed algorithm allows improvement in reduction of CO2 emissions by 9% comparatively to RED WoLF double threshold approach and by 26% comparatively to RED WoLF single threshold approach. Besides, the proposed technique is at least 100 times faster than linear optimisation, making the algorithm applicable to edge systems. The proposed method is later tested in numerical experiment on two measured datasets from Luxembourg school and office, equipped with batteries and ground source heat pumps. The system allows the reduction of CO2 emission and improvement of self-consumption, size reduction of the photovoltaic array installed at the facilities by at least by half as well as substituting battery storage by thermal storage, reducing the initial investment to the system. Intriguingly, despite 3.6 times difference in efficiency between heat pumps and storage heaters, the system equipped with latter have potential to achieve similar performance in carbon reduction, suggesting that energy storage have more prominent carbon reduction effect, than the power consumption, making cheaper systems with storage heaters a possible alternative to heat pumps.

User Selection and Power Allocation Scheme With SINR-Based Deep Learning for Downlink NOMA

In non-orthogonal multiple access (NOMA) systems, transmit power allocation plays a crucial role in maximizing the sum rate, while satisfying quality of service requirements of users. In prior study, an interior point method (IPM) has been presented as an iterative algorithm for power allocation, which can maximize the sum rate and minimize the outage rate. However, such iterative algorithms typically suffer from low computational efficiency and excessively high latency. To overcome these limitations, machine learning-based power allocation schemes have been widely studied. Along the same line, in this paper, focusing on unsupervised learning to improve the computational complexity for power allocation as well as user selection, we propose a deep neural network (DNN)-based joint user selection and power allocation technique for the cellular downlink multiple-input single-output(MISO) NOMA systems, where the transmit antenna selection and multi-cell cooperation are considered. Especially, an optimization problem for user selection and power allocation is formulated to maximize the sum rate under the constraint of minimum data-rate requirement. We propose a new loss function and training model for user selection and power allocation to solve the optimization problem, where the training and testing models are based on the signal-to-interference-plus-noise-ratio (SINR) information instead of channel state information, which can significantly reduce the input data size in DNN. Through simulations, we show that our proposed scheme provides comparable performances in terms of sum rate and outage rate to the optimal solutions, while requiring lower computational complexity compared to the optimal ones.

Suboptimal Safety-Critical Control for Continuous Systems Using Prediction–Correction Online Optimization

This article presents an innovative efficient safety-critical control scheme for nonlinear systems by combining techniques of control barrier function (CBF) and online time-varying optimization. The idea lies in that when directly calling the complete optimization solvers used in the CBF method, such as CBF-based quadratic programming (CBF-QP), is computationally inefficient for complex tasks, the suboptimal solutions obtained from online learning techniques can be an alternatively reliable choice for ensuring both efficiency and control performance. By using the barrier-based interior point method, the original optimization problem with CBF constraints is reduced to an unconstrained one with approximate optimality. Then, Newton-and gradient-based continuous dynamics are introduced to generate alternative cheap solutions while ensuring safety. By further considering the lag effect of online tracking, a prediction term is added to the dynamics. In this way, the online cheap solutions are proven to exponentially converge to the time-varying suboptimal solutions of the interior point method. Furthermore, the safety criteria are established, and the robustness of the designed algorithms is analyzed theoretically. Finally, the effectiveness is illustrated by conducting two experiments on obstacle avoidance and anti-swing tasks.

Permutation Matrix Modulation

We propose a novel scheme that allows MIMO system to modulate a set of permutation matrices to send more information bits, extending our initial work on the topic. This system is called Permutation Matrix Modulation (PMM). The basic idea is to employ a permutation matrix as a precoder and treat it as a modulated symbol. We continue the evolution of index modulation in MIMO by adopting all-antenna activation and obtaining a set of unique symbols from altering the positions of the antenna transmit power. We provide the analysis of the achievable rate of PMM under Gaussian Mixture Model (GMM) distribution \revv{and finite cardinality input (FCI). Numerical results are evaluated by comparing PMM with the other existing systems.} We also present a way to attain the optimal achievable rate of PMM by solving a maximization problem via interior-point method. A low complexity detection scheme based on zero-forcing (ZF) is proposed, and maximum likelihood (ML) detection is discussed. We demonstrate the trade-off between simulation of the symbol error rate (SER) and the computational complexity where ZF performs worse in the SER simulation but requires much less computational complexity than ML.

Fast Model Predictive Control System for Wave Energy Converters With Wave Tank Tests

At present, the mainstream solution for the control of wave energy converters (WECs), the model predictive control (MPC)-like method, faces a gap between simulation-based research and practical application. Two of the major difficulties are the online computation burden and the requirement of real-time wave information. In this study, a fast solving strategy is proposed at the level of quadratic programming (QP), where a tailored warm-start algorithm is designed and combined with an early stop technique. Simulations show that only one iteration of interior-point method (IPM) suffices to reach over 95% efficiency of the exact MPC, which significantly speeds up the computation. The fast strategy is then deployed on the real-time controller of a prototype WEC platform. During this implementation, the instantaneous wave force is estimated by a Kalman filter entirely based on the basic feedback signals: position, velocity, and the generator current, while future wave forces are predicted by an autoregressive model. The wave tank test confirms that the proposed fast MPC is capable of being executed at a high frequency, achieving stable operations within constraints, and reaching satisfactory energy efficiency under real wave-body interactions.

Efficiency-Boosting Federated Learning in Wireless Networks: A Long-Term Perspective

Federated learning (FL) can train a global model from clients' local dataset, which can make full use of the computing resources of clients and performs more extensive and efficient machine learning applications on clients with protecting user information requirements. Many existing works have focused on optimizing FL accuracy within the resource constrained in each individual round. However there are few works comprehensively consider the optimization for latency, accuracy and energy consumption from a long-term perspective in wireless federated learning. Inspired by this, in this paper, we investigate FL in wireless networks where client selection and bandwidth allocation are two crucial factors for improving the FL accuracy as well as reducing latency and energy consumption. We formulate the optimization problem as a mixed-integer problem, which minimizes the cost function over finite rounds while satisfying energy budget constraints of each client from a long-term perspective. To address this optimization problem, we propose the Per-round Energy Drift Plus Cost (PEDPC) algorithm in an online manner, including two parts: client selection and bandwidth allocation, which can be addressed by Increasing Time-Maximum Client Selection (ITMCS) algorithm and Barrier Method, respectively. Finally, the performance of the PEDPC algorithm is verified by extensive simulations in terms of latency, accuracy and energy consumption in IID and NON-IID data distributions.

Regularization Strategy Aided Robust Unsupervised Learning for Wireless Resource Allocation

Unsupervised learning (UL) is widely used in the wireless resource allocation problems due to its lower computational complexity and better performance compared with traditional optimization algorithms. Since wireless resource allocation problems usually have several constraints, primal-dual learning based UL framework are widely adopted. However, the primal-dual learning approach has the problem of oscillation around the constraint threshold while training and there may be serious constraint violations when deployment. In addition, although the output of the neural network can also be restricted to the feasible region by the penalty function method, the optimality of such training methods cannot be guaranteed. In this paper, we combine the primal dual learning method with the penalty function method and propose a regularized unsupervised learning (RUL) framework to enhance the robustness of the primal-dual learning based UL framework. In the proposed RUL framework, we use regularization techniques to improve the robustness of primal-dual learning by reducing the risk of constraint violations while training. A quadratic penalty term is introduced into the Lagrangian function of the wireless optimization problem where the constraints can be equivalent to equality constraints to form its augmented Lagrangian function. In the simulation, we give a simple point to point power optimization problem as an example to show that the proposed RUL can improve the robustness of constraint convergence, and can also accelerate training speed.

Minimum path deviation rapid online path planning of unmanned aerial vehicles with avoidance zones constraints

This paper investigates a minimum path deviation online path planning problem for UAV with constrainted avoidance zones. The nonlinear and nonconvex of this problem make the path planning is very time consuming and not acceptable for using onboard. Three new state variables and two control variables are redefined to convert the nonconvex problem into a second-order cone convex programming problem, which can be solved in polynomial time by primal-dual interior-point method, theoretical proof demonstrates the equivalence of the relaxed convex problem and the original problem. We propose a sequential second-order cone programming algorithm in order to get the optimal solution of the convexified problem. Numerical simulations show the effectiveness and less time-consuming of the proposed algorithm, no initial guess required and efficient solving process indicate that the algorithm has potential future for online path planning applications.

Numerical investigation of interactions between hydraulic and pre-existing opening-mode fractures in crystalline rocks based on a hydro-grain-based model

Hot dry rock (HDR) is deep geothermal reservoir rock predominantly containing granite, whose physical and mechanical properties are governed by heterogeneous crystal structures. However, the fluid conductivity of intact granite with ultra-low permeability cannot be reformed using existing techniques. Complex fracture networks must be created by connecting hydraulic fractures with natural fractures developed in reservoirs. In this study, we introduce the wall barrier method into the novel hydro-grain-based model (hydro-GBM) to build a prefractured granite model at the mineral grain scale. This model enables investigation of the effects of the stress environment, mineral spatial distribution, and fluid injection rate on hydraulic fracturing characteristics. Microcracks around the inner tips of pre-existing fractures reproduce the initiation, propagation, and coalescence behaviors similar to experimental results. Mineral spatial distributions induce random changes in the propagation paths of hydraulic fractures. Increasing the fluid injection rate delays the deflection of hydraulic fractures and extends the propagation distance along the major axes of pre-existing fractures. The average activity level and proportion of large seismic events are reduced by injecting low-rate fluid. In summary, our results reveal the interactions between hydraulic and pre-existing fractures and provide a valuable reference for constructing an efficient enhanced geothermal system (EGS) for deep reservoirs.

Tailored presolve techniques in branch‐and‐bound method for fast mixed‐integer optimal control applications

AbstractMixed‐integer model predictive control (MI‐MPC) can be a powerful tool for controlling hybrid systems. In case of a linear‐quadratic objective in combination with linear or piecewise‐linear system dynamics and inequality constraints, MI‐MPC needs to solve a mixed‐integer quadratic program (MIQP) at each sampling time step. This paper presents a collection of exact block‐sparse presolve techniques to efficiently remove decision variables, and to remove or tighten inequality constraints, tailored to mixed‐integer optimal control problems. In addition, we describe a novel approach based on a heuristic presolve algorithm to compute a feasible but possibly suboptimal MIQP solution. We present benchmarking results for a C code implementation of the proposed BB‐ASIPM solver, including a branch‐and‐bound (B&B) method with the proposed tailored presolve techniques and an active‐set based interior point method (ASIPM), compared against multiple state‐of‐the‐art MIQP solvers on a case study of motion planning with obstacle avoidance constraints. Finally, we demonstrate the feasibility and computational performance of the BB‐ASIPM solver in embedded system on a dSPACE Scalexio real‐time rapid prototyping unit for a second case study of stabilization for an underactuated cart‐pole with soft contacts.

A New full-newton step infeasible interior-point method for P∗(κ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_*(\\kappa )$$\\end{document}-linear Complementarity problem

In this paper, we suggest a new infeasible interior-point method (IIPM) for P∗(κ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{*}(\\kappa )$$\\end{document}-linear complementarity problem (P∗(κ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{*}(\\kappa )$$\\end{document}-LCP) based on a new class of kernel functions with full-Newton steps. Each iteration of the algorithm consists of a feasible step and a few centering steps. The feasible step is defined by the newly proposed kernel functions, while the centering step is determined by using Newton’s method. New class of kernel functions includes a logarithmic kernel function in Roos (SIAM J Optim 16:1110–1136, 2006) and a trigonometric kernel function in Moslemi and Kheirfam (Optim Lett 13:127–157, 2019), Kheirfam and Haghighi (Commun Comb Optim 3:51–70, 2018), Fathi-Hafshejani et al. (J Appl Math Comput 48:111–128, 2015) as special cases. And we show that the proposed algorithm has the best known complexity for P∗(κ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_*(\\kappa )$$\\end{document}-LCP for such a method and present some numerical results.

Analysis of Vibration-Damping Characteristics and Parameter Optimization of Cylindrical Cavity Double-Plate Phononic Crystal.

For the application of low-frequency vibration damping in industry, a cylindrical cavity double-layer plate-type local resonance phononic crystal structure is proposed to solve low-frequency vibration in mechanical equipment. Initially, using COMSOL 5.4 software, the bending wave band gap is calculated in conjunction with elastic dynamics theory and the BOLOCH theorem to be 127-384 Hz. Then the mechanism of bending wave gap is analyzed by combining element mode shape and an equivalent model. Subsequently, the bending vibration transmission characteristics of the crystal plate are explained, and the vibration-damping characteristics are illustrated in combination with the time-frequency domain. An experimental system is constructed to verify the vibration-damping properties of crystal plates; the experimental results and simulation results are verified with each other. Finally, the element structural parameters are optimized using the RSM. Fifty-four sets of experiments are designed based on six structural factors and three levels, and the expressions between the bending wave band gap and six structural factors are obtained. Combining the particle swarm algorithm, the optimization is performed with the band gap width as the target. This method is shown to be more accurate than the commonly used interior point method. The structure of cylindrical-cavity-type phononic crystal and the parameter optimization method proposed in this paper provide a certain reference for the design of local-resonance-type phononic crystal.

Self-Supervised Primal-Dual Learning for Constrained Optimization

This paper studies how to train machine-learning models that directly approximate the optimal solutions of constrained optimization problems. This is an empirical risk minimization under constraints, which is challenging as training must balance optimality and feasibility conditions. Supervised learning methods often approach this challenge by training the model on a large collection of pre-solved instances. This paper takes a different route and proposes the idea of Primal-Dual Learning (PDL), a self-supervised training method that does not require a set of pre-solved instances or an optimization solver for training and inference. Instead, PDL mimics the trajectory of an Augmented Lagrangian Method (ALM) and jointly trains primal and dual neural networks. Being a primal-dual method, PDL uses instance-specific penalties of the constraint terms in the loss function used to train the primal network. Experiments show that, on a set of nonlinear optimization benchmarks, PDL typically exhibits negligible constraint violations and minor optimality gaps, and is remarkably close to the ALM optimization. PDL also demonstrated improved or similar performance in terms of the optimality gaps, constraint violations, and training times compared to existing approaches.

Policy-Based Primal-Dual Methods for Convex Constrained Markov Decision Processes

We study convex Constrained Markov Decision Processes (CMDPs) in which the objective is concave and the constraints are convex in the state-action occupancy measure. We propose a policy-based primal-dual algorithm that updates the primal variable via policy gradient ascent and updates the dual variable via projected sub-gradient descent. Despite the loss of additivity structure and the nonconvex nature, we establish the global convergence of the proposed algorithm by leveraging a hidden convexity in the problem, and prove the O(T^-1/3) convergence rate in terms of both optimality gap and constraint violation. When the objective is strongly concave in the occupancy measure, we prove an improved convergence rate of O(T^-1/2). By introducing a pessimistic term to the constraint, we further show that a zero constraint violation can be achieved while preserving the same convergence rate for the optimality gap. This work is the first one in the literature that establishes non-asymptotic convergence guarantees for policy-based primal-dual methods for solving infinite-horizon discounted convex CMDPs.

A Newton-CG Based Barrier Method for Finding a Second-Order Stationary Point of Nonconvex Conic Optimization with Complexity Guarantees

A Newton-CG Based Barrier Method for Finding a Second-Order Stationary Point of Nonconvex Conic Optimization with Complexity Guarantees

The Control Method of Autonomous Flight Avoidance Barriers of UAVs in Confined Environments

This paper proposes an improved 3D-Vector Field Histogram (3D-VFH) algorithm for autonomous flight and local obstacle avoidance of multi-rotor unmanned aerial vehicles (UAVs) in a confined environment. Firstly, the method employs a target point coordinate system based on polar coordinates to convert the point cloud data, considering that long-range point cloud information has no effect on local obstacle avoidance by UAVs. This enables UAVs to effectively utilize obstacle information for obstacle avoidance and improves the real-time performance of the algorithm. Secondly, a sliding window algorithm is used to estimate the optimal flight path of the UAV and implement obstacle avoidance control, thereby maintaining the attitude stability of the UAV during obstacle avoidance flight. Finally, experimental analysis is conducted, and the results show that the UAV has good attitude stability during obstacle avoidance flight, can autonomously follow the expected trajectory, and can avoid dynamic obstacles, achieving precise obstacle avoidance.