Sequential Quadratic Programming Method Research Articles

Buffer Occupancy-Based Congestion Control Protocol for Wireless Multimedia Sensor Networks

Wireless multimedia sensor networks (WMSNs) have stringent constraints and need to deliver data packets to the sink node within a predefined limited time. However, due to congestion, buffer overflow occurs and leads to the degradation of the quality-of-service (QoS) parameters of event information. Congestion in WMSNs results in exhausted node energy, degraded network performance, increased transmission delays, and high packet loss. Congestion occurs when the volume of data trying to pass through a network exceeds its capacity. First, the BOCC protocol uses two congestion indicators to detect congestion. One is the buffer occupancy and other is the buffer occupancy change rate. Second, a rate controller is proposed to protect high-priority I-frame packets during congestion. BOCC sends a congestion notification to the source node to reduce congestion in the network. The source node adjusts its data transmission rate after receiving the congestion notification message. In the proposed algorithm, the rate adjustment is made by discarding low-priority P-frame packets from the source nodes. Third, to further improve the performance of the BOCC protocol, the problem is formulated as a constrained optimization problem and solved using convex optimization and sequential quadratic programming (SQP) methods. Experimental results based on Raspberry Pi sensor nodes show that the BOCC protocol achieves up to 16% reduction in packet loss and up to 23% reduction in average end-to-end delay compared to state-of-the-art congestion control algorithms.

Machining error compensation of free-form surfaces by combination of ordinary kriging method and mirror compensation method

ABSTRACT Improving the accuracy and efficiency of free-form surface machining is a common goal of modern manufacturing. In this study, a compensation method combining the ordinary kriging method based on sequential quadratic programming method optimization (SQP-OK) and the mirror compensation method for machining errors of free-form workpieces was applied, with the aim of significantly improving the workpiece machining accuracy. Machining errors on the surface of the workpiece were predicted utilizing the SQP-OK after the workpieces were completed with semi-finishing machining based on the on-machine measurement (OMM) results of the workpiece. Based on the prediction result, the mirror compensation method was applied to calculate the compensation points. Free-form workpieces were compensated for by modifying the NC code for semi-finishing. To verify the effectiveness of the proposed method, two free-form workpieces were machined with computer numerical control (CNC) compensation, applying the proposed method and the method modifying the overall machining allowance. The experimental results revealed that the compensation method proposed in this paper reduced the average value of the machining errors decreased by 28.6% in absolute value, 31.1% in maximum undercut, and 28.8% in maximum overcut for the free-form workpiece, respectively, compared with the compensation method of modifying the overall machining allowance.

CO2 emissions of fuel-cell battery hybrid system for large ships

ABSTRACT The needs of solid oxide fuel cells (SOFC) and batteries in large ships are analyzed by estimating the amount of fuel consumption and CO2 emissions. Three types of systems are proposed: 1) fuel cells-battery-generator engine system, 2) battery-generator engine system, and 3) generator engine system. This study is based on the time-varying electric power demand and adopted the sequential quadratic programming (SQP) method to find the optimal power distribution of mixed power sources. CO2 emissions in the SOFC hybrid system are 11.6% lower than in the conventional generator engine system, and those in the battery-generator engine system are 5.1% lower than in the conventional system. The reduction of CO2 emissions come from three factors: the operation of the generator engine at a relatively high load rate, the battery sharing the operation of the generator engine, and the high efficiency of the SOFC running. The SOFC hybrid system can be a sustainable technology in large vessels.

Comparative study of kernel- and deep learning-based proxy models for nonlinearly constrained life-cycle production optimization

This study presents a comparative study for the application of deep learning–based and kernel-based proxy models in hydrocarbon production optimization with nonlinear constraints, comparing their performance against high-fidelity simulators (HFS) in terms of computational efficiency and the quality of the results achieved. One of the proxy models employed is referred to as embed to control and observe (E2CO), a deep learning–based model. The other model is a kernel-based proxy model known as least-squares support-vector regression (LS-SVR). Both proxy models can predict production/injection outputs for each well. We use the sequential quadratic programming (SQP) method for nonlinearly constrained production optimization. Our optimization objective revolves around the net present value (NPV), while the nonlinear state constraints involve field liquid production rate (FLPR) and field water production rate (FWPR). NPV, FLPR, and FWPR are estimated using two different types of proxy models. The gradient of the objective function and the Jacobian matrix of constraints are computed analytically for LS-SVR. In contrast, the method of stochastic simplex approximated gradient (StoSAG) is employed for optimization with E2CO and HFS. The reservoir model considered in this study is a two-phase, three-dimensional reservoir characterized by channelized and heterogeneous permeability, sourced from the SPE10 benchmark case. We optimize well controls to maximize NPV in an oil-water waterflooding scenario. All proxy models can achieve optimal NPV results like those obtained through HFS but with significantly lower computational resources. Both proxy models are found to be approximately 15-fold more efficient than using HFS when the number of simulation runs is compared. Forward prediction results show that both proxy models outperform numerical simulator, and the E2CO can predict up to 2400 times faster than HFS whereas speedups gained over HFS go up to 5000-fold with LS-SVR. The training time required for E2CO is at least an order of magnitude longer than that for LS-SVR. The main contributions of the paper are (i) development of a novel methodology that uses an E2CO proxy model within a gradient-based iterative retraining proxy approach for life-cycle production optimization with nonlinear state constraints, (ii) comparison of this methodology in terms of computational cost and accuracy with an LS-SVR proxy model, and (iii) new insights into the accuracy and prediction performances of these machine learning-based proxy models for 3D oil-water systems as well as their efficiency in nonlinearly constrained production optimization for waterflooding applications.

Local quadratic convergence of the SQP method for an optimal control problem governed by a regularized fracture propagation model

We prove local quadratic convergence of the sequential quadratic programming (SQP) method for an optimal control problem of tracking type governed by one time step of the Euler-Lagrange equation of a time discrete regularized fracture or damage energy minimization problem. This lower-level energy minimization problem % describing the fracture process contains a penalization term for violation of the irreversibility condition in the fracture growth process and a viscous regularization term. Conditions on the latter, corresponding to a time step restriction, guarantee strict convexity and thus unique solvability of the Euler Lagrange equations. Nonetheless, these are quasilinear and the control problem is nonconvex. For the convergence proof with $L^\infty$ localization of the SQP-method, we follow the approach from \cite{Troeltzsch:1999}, utilizing strong regularity of generalized equations and arguments from \cite{HoppeNeitzel:2020} for $L^2$-localization. 2020 Mathematics Subject Classification 90C55, 49M41, 49M15.

Stabilized SQP Methods in Hilbert Spaces

Based on techniques by (S.J. Wright 1998) for finite-dimensional optimization, we investigate a stabilized sequential quadratic programming method for nonlinear optimization problems in infinite-dimensional Hilbert spaces. The method is shown to achieve fast local convergence even in the absence of a constraint qualification, generalizing the results obtained by (S.J. Wright 1998 and W.W. Hager 1999) in finite dimensions to this broader setting.

An improved sequential quadratic programming method for identifying the total heat exchange factor of reheating furnace

Accurate identification of the total heat exchange factor (THEF), which serves as the foundation for online control data in the reheating furnace, holds significant importance for enhancing the digitization and intelligence level of the furnace, mitigating environmental pollution, and improving the economic performance of enterprises. For this purpose, based on the theory of inverse heat transfer problem, a solver combining Sequential Quadratic Programming and Broyden Combined Method (SQPBC) was developed to accurately identify high-dimensional and strongly nonlinear THEF in the reheating furnace. Integrating the efficient Broyden Combined Method (BCM) into Sequential Quadratic Programming (SQP) enables the rapid and accurate estimation of the Jacobian matrix to effectively enhance computational speed without compromising accuracy. Experimental data has been employed to validate the accuracy of the inversion results. The performance of SQPBC has been comprehensively analyzed through a series of numerical experiments, with a particular focus on investigating the impact of sampling frequency and sensor location on the inversion results. The findings reveal that after reducing the sampling period to 2 min, further decreasing the sampling period has a minor effect on the average relative error of the identification results; the closer the measurement points are to the surface of the slab, the more accurate the identification of THEF on the slab's surface.

Adaptive fractional-order nonsingular terminal sliding mode control and sequential quadratic programming torque distribution for lateral stability of FWID-EVs with actuator constraints

This paper proposes a novel sliding mode control (SMC) algorithm for direct yaw moment control of four-wheel independent drive electric vehicles (FWID-EVs). The algorithm integrates adaptive law theory, fractional-order theory, and nonsingular terminal sliding mode reaching law theory to reduce chattering, handle uncertainty, and avoid singularities in the SMC system. A sequential quadratic programming (SQP) method is also proposed to optimize the yaw moment distribution under actuator constraints. The performance of the proposed algorithm is evaluated by a hardware-in-the-loop test with two driving maneuvers and compared with two existing SMC-based schemes together with the cases with the change of vehicle parameters and disturbances. The results demonstrate that the proposed algorithm can eliminate chattering and achieve the best lateral stability as compared with the existing schemes.

High-Speed Motion Planning with Object Acceleration Constraint for Industrial Robots

In this paper, we propose a new approach to efficiently plan trajectories for industrial robots, where total trajectory time is reduced while limiting the robot end-effector acceleration to a safe threshold, which guarantees an object to be transported safely without damage or spills. We also propose to solve the optimization problem in two steps by utilizing both the quadratic programming algorithm and sparse sequential quadratic programming method. The proposed two-step procedure empirically proves that computing time of solving the optimization problem is significantly reduced. Effectiveness of the proposed approach was verified in Drake, where the obtained results are highly promising.

Chaos-infused wind power integration in the grey wolf optimal paradigm for combine thermal-wind power plant systems

This research presents a novel methodology for tackling the combined thermal-wind economic load dispatch (ELD) issue in contemporary power system. The proposed approach involves hybridizing active-set algorithm (ASA), interior point algorithm (IPA) and sequential quadratic programming (SQP) into grey wolf optimization (GWO) algorithm, while effectively incorporating the intricacies associated with renewable energy sources (RES). A more accurate model is made possible by hybridization for complex systems with memory and hereditary characteristics. The GWO is used as a tool for global search while ASA, IPA and SQP methods are used for rapid local optimization mechanism. The performance evaluation of the design heuristics is carried out on 37 thermal and 3 wind power generating units and outcomes endorse the effectiveness of the proposed scheme over state-of-the-art counterparts. The worthy performance is further validated on statistical assessments in case of thermal-wind integrated ELD problem in terms of measure of central tendency and variation on cost and complexity indices.

A non-overlapping optimization-based domain decomposition approach to component-based model reduction of incompressible flows

We present a component-based model order reduction procedure to efficiently and accurately solve parameterized incompressible flows governed by the Navier-Stokes equations. Our approach leverages a non-overlapping optimization-based domain decomposition technique to determine the control variable that minimizes jumps across the interfaces between sub-domains. To solve the resulting constrained optimization problem, we propose both Gauss-Newton and sequential quadratic programming methods, which effectively transform the constrained problem into an unconstrained formulation. Furthermore, we integrate model order reduction techniques into the optimization framework, to speed up computations. In particular, we incorporate localized training and adaptive enrichment to reduce the burden associated with the training of the local reduced-order models. Numerical results are presented to demonstrate the validity and effectiveness of the overall methodology.

The Design and Optimization of Additively Manufactured Radial Compressor of a Miniature Gas Turbine Engine

Abstract This paper presents a multidisciplinary design methodology for a single-stage radial compressor of a small-scale gas turbine jet engine. The entire engine, producing more than 600 N thrust with an engine diameter of less than 30 cm, will be manufactured by additive manufacturing (AM) in a single piece. Therefore, it is crucial to pinpoint the design limitations that may arise due to the AM methods. The preliminary design calculations are carried out in the Von Karman Institute for Fluid Dynamics (VKI's) in-house centrifugal compressor off-design (CCOD) code. The detailed design and optimization studies coupled with computational fluid dynamics (CFD) simulations are performed to improve the aerodynamic performance of the radial compressor by using the sequential quadratic programming (SQP) method with an Adjoint solver in the VKI's in-house computer aided design and optimization (CADO) tool. In the final design, a large increase in thrust is obtained and the manufacturing constraints are satisfied.

A fast and accurate domain decomposition nonlinear manifold reduced order model

This paper integrates nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD). NM-ROMs approximate the full order model (FOM) state in a nonlinear-manifold by training a shallow, sparse autoencoder using FOM snapshot data. These NM-ROMs can be advantageous over linear-subspace ROMs (LS-ROMs) for problems with slowly decaying Kolmogorov n-width. However, the number of NM-ROM parameters that need to be trained scales with the size of the FOM. Moreover, for “extreme-scale” problems, the storage of high-dimensional FOM snapshots alone can make ROM training expensive. To alleviate the training cost, this paper applies DD to the FOM, computes NM-ROMs on each subdomain, and couples them to obtain a global NM-ROM. This approach has several advantages: Subdomain NM-ROMs can be trained in parallel, involve fewer parameters to be trained than global NM-ROMs, require smaller subdomain FOM dimensional training data, and can be tailored to subdomain-specific features of the FOM. The shallow, sparse architecture of the autoencoder used in each subdomain NM-ROM allows application of hyper-reduction (HR), reducing the complexity caused by nonlinearity and yielding computational speedup of the NM-ROM. This paper provides the first application of NM-ROM (with HR) to a DD problem. In particular, this paper details an algebraic DD reformulation of the FOM, training a NM-ROM with HR for each subdomain, and a sequential quadratic programming (SQP) solver to evaluate the coupled global NM-ROM. Theoretical convergence results for the SQP method and a priori and a posteriori error estimates for the DD NM-ROM with HR are provided. The proposed DD NM-ROM with HR approach is numerically compared to a DD LS-ROM with HR on the 2D steady-state Burgers’ equation, showing an order of magnitude improvement in accuracy of the proposed DD NM-ROM over the DD LS-ROM.

Multi-Energy Flow Integrated Energy System Considering Economic Efficiency Targets: Capacity Allocation and Scheduling Study

An integrated energy system (IES) breaks down barriers between different energy subsystems, enhancing energy reliability and efficiency. However, issues such as uneven equipment capacity allocation and suboptimal scheduling persist in multi-energy flow IES. To maximize economic benefits while ensuring energy balance and the operational characteristics of the equipment, a capacity matching optimization and scheduling strategy model for IES was developed. Firstly, mathematical models for the electricity, gas, and thermal networks within the IES were established. Secondly, considering the efficiency of energy conversion between different forms and constraints of energy storage in the electricity–thermal–gas interconnected energy system, optimization solutions were obtained using regional contraction algorithms and sequential quadratic programming methods. Finally, case studies conducted in a real park demonstrated that, through optimized capacity matching, unit prices for electricity, heat, and gas decreased by 39.9%, 90.5%, and 74.2%, respectively, effectively improving the economic viability of the system.

An efficient solver for the inverse kinematics of cable-driven manipulators with pure rolling joints using a geometric iterative approach

The inverse kinematics (IK) problem of cable-driven manipulators with pure rolling joints (CDM-PRJs) presents unique challenges due to the equal angle constraints and strict joint limits. These factors render existing IK solvers ineffective or result in substantial degradation of their performance. To address these challenges, we propose a three-phase geometric iterative method to efficiently solve the IK problem for CDM-PRJs, which is a variant of the forward and backward reaching inverse kinematics method. Our method begins by establishing a surrogate model for CDM-PRJs to handle the equal angle constraints. Subsequently, we introduce a geometric iterative approach comprising a forward reaching phase, a backward reaching phase, and a state update phase. Additionally, we devise two novel measures, the random disturbance measure and the branch change measure, to effectively address deadlock situations and asymmetric joint limits, respectively. Simulation results demonstrate that our method surpasses the inverse Jacobian method and the sequential quadratic programming method in terms of success rate and computational efficiency. Furthermore, our method exhibits generality across various CDM-PRJs.

A projected-search interior-point method for nonlinearly constrained optimization

AbstractThis paper concerns the formulation and analysis of a new interior-point method for constrained optimization that combines a shifted primal-dual interior-point method with a projected-search method for bound-constrained optimization. The method involves the computation of an approximate Newton direction for a primal-dual penalty-barrier function that incorporates shifts on both the primal and dual variables. Shifts on the dual variables allow the method to be safely “warm started” from a good approximate solution and avoids the possibility of very large solutions of the associated path-following equations. The approximate Newton direction is used in conjunction with a new projected-search line-search algorithm that employs a flexible non-monotone quasi-Armijo line search for the minimization of each penalty-barrier function. Numerical results are presented for a large set of constrained optimization problems. For comparison purposes, results are also given for two primal-dual interior-point methods that do not use projection. The first is a method that shifts both the primal and dual variables. The second is a method that involves shifts on the primal variables only. The results show that the use of both primal and dual shifts in conjunction with projection gives a method that is more robust and requires significantly fewer iterations. In particular, the number of times that the search direction must be computed is substantially reduced. Results from a set of quadratic programming test problems indicate that the method is particularly well-suited to solving the quadratic programming subproblem in a sequential quadratic programming method for nonlinear optimization.

Методы с суженной матрицей Гессе как возмущенный метод Ньютона–Лагранжа

For an equality-constrained optimization problem, we consider the possibility to interpret sequential quadratic programming methods employing the Hessian of the Lagrangian reduced to the null space of the constraints’ Jacobian, as a perturbed Newton–Lagrange method. We demonstrate that such interpretation with required estimates on perturbations is possible for certain sequences generated by variants of these methods making use of second-order corrections. This allows to establish, from a general perspective, superlinear convergence of such sequences, the property generally missing for the main sequences of the methods in question.

An Inexact Sequential Quadratic Programming Method for Learning and Control of Recurrent Neural Networks.

This article considers the two-stage approach to solving a partially observable Markov decision process (POMDP): the identification stage and the (optimal) control stage. We present an inexact sequential quadratic programming framework for recurrent neural network learning (iSQPRL) for solving the identification stage of the POMDP, in which the true system is approximated by a recurrent neural network (RNN) with dynamically consistent overshooting (DCRNN). We formulate the learning problem as a constrained optimization problem and study the quadratic programming (QP) subproblem with a convergence analysis under a restarted Krylov-subspace iterative scheme that implicitly exploits the structure of the associated Karush-Kuhn-Tucker (KKT) subsystem. In the control stage, where a feedforward neural network (FNN) controller is designed on top of the RNN model, we adapt a generalized Gauss-Newton (GGN) algorithm that exploits useful approximations to the curvature terms of the training data and selects its mini-batch step size using a known property of some regularization function. Simulation results are provided to demonstrate the effectiveness of our approach.

A sequential quadratic programming based strategy for particle swarm optimization on single-objective numerical optimization

Over the last decade, particle swarm optimization has become increasingly sophisticated because well-balanced exploration and exploitation mechanisms have been proposed. The sequential quadratic programming method, which is widely used for real-parameter optimization problems, demonstrates its outstanding local search capability. In this study, two mechanisms are proposed and integrated into particle swarm optimization for single-objective numerical optimization. A novel ratio adaptation scheme is utilized for calculating the proportion of subpopulations and intermittently invoking the sequential quadratic programming for local search start from the best particle to seek a better solution. The novel particle swarm optimization variant was validated on CEC2013, CEC2014, and CEC2017 benchmark functions. The experimental results demonstrate impressive performance compared with the state-of-the-art particle swarm optimization-based algorithms. Furthermore, the results also illustrate the effectiveness of the two mechanisms when cooperating to achieve significant improvement.

An efficient and provable sequential quadratic programming method for American and swing option pricing

A sequential quadratic programming numerical method is proposed for American option pricing based on the variational inequality formulation. The variational inequality is discretized using the θ-method in time and the finite element method in space. The resulting system of algebraic inequalities at each time step is solved through a sequence of box-constrained quadratic programming problems, with the latter being solved by a globally and quadratically convergent, large-scale suitable reflective Newton method. It is proved that the sequence of quadratic programming problems converges with a constant rate under a mild condition on the time step size. The method is general in solving the variational inequalities for the option pricing with many styles of optimal stopping and complex underlying asset models. In particular, swing options and stochastic volatility and jump diffusion models are studied. Numerical examples are presented to confirm the effectiveness of the method.