Sequential Quadratic Programming Method Research Articles

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.

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.

Nonlinear robust distribution planning model for perishable products based on sustainable development

With the development of social economy and the improvement of people living standards, the distribution of cold chain products has become increasingly prominent. In the process of distribution of cold chain products, due to its perishable nature, it is not only necessary to consider the efficiency and economy of transportation, but also to pay attention to risk aversion factors. Therefore, the stochastic programming of cold chain logistics based on risk aversion has become an urgent problem to be solved. Aiming to minimize the economic cost and transform the carbon emission level of cold chain transportation into carbon emission cost, a distributionally robust mean-conditional value-at-risk optimization model for the perishable goods distribution management problem is established, in which the partial distribution information of uncertain demand and transportation environment temperature was known. Then a computationally tractable equivalence model is obtained under the box ambiguity set. For the proposed nonlinear model, a trust region sequential quadratic programming method with filter is proposed to solve it. Finally, through a case study, the relationship between the stochastic programming model and the distributionally robust model is analysed.

A Time-Optimal Continuous Jerk Trajectory Planning Algorithm for Manipulators

In this paper, we propose a new optimal trajectory planning method for the manipulator to optimize its operating efficiency and ensure the smoothness of the motion process. The position sequences in joint space corresponding to a specified trajectory in task space are obtained by using the inverse kinematic algorithm, and the seventh-degree B-spline curve interpolation method is used to construct the joint trajectory with controllable start–stop kinematic parameters, and continuous velocity, acceleration and jerk. The kinematic constraints of the manipulator are transformed into the control point constraints of the B-spline curve, the sequential quadratic programming method is used to solve the optimal motion time node, and then the time-optimal continuous jerk trajectory satisfying the nonlinear kinematic constraints is planned. Simulation results show that the proposed trajectory planning method provides the ideal trajectory for the joint controller, ensuring the manipulator can smoothly track any specified trajectory in the task space in the shortest time.

Adaptive shape optimization with NURBS designs and PHT-splines for solution approximation in time-harmonic acoustics

In this paper, we propose the adaptive shape optimization algorithm based on the concept of Geometry Independent Field approximaTion paired with the Sequential Quadratic Programming method, applied to time-harmonic acoustics.Non-Uniform Rational Basis Splines are used for the geometry parametrization, and in the same manner, as in conventional isogeometric shape optimization, the control points of the optimized boundary serve as design variables. This preserves the tight link between the design, analysis, and optimization models. Polynomial splines over Hierarchical T-meshes are employed for the solution approximation, providing the capability to refine the solution locally and adaptively to the boundary changes during the optimization process in a step-by-step procedure controlled by the error tolerance. This leads to significant savings in terms of the number of degrees of freedom and computational time.The performance of the proposed method is demonstrated in three benchmark examples and the results are compared with the data from the literature, showing the high accuracy and efficiency of the technique. It is shown that an adaptive optimization scheme can bring over 90% reduction in both, the number of degrees of freedom and time, in comparison with the uniform refinement.

Improving Directional Overcurrent Relay Coordination in Distribution Networks for Optimal Operation Using Hybrid Genetic Algorithm with Sequential Quadratic Programming

In recent years, with the growing popularity of smart microgrids in distribution networks, the effective coordination of directional overcurrent relays (DOCRs) has presented a significant challenge for power system operators due to the intricate and nonlinear nature of their optimization model. Hence, this study proposes a hybrid GA-SQP algorithm to enhance the coordination of directional overcurrent relays (DOCRs) in radial and non-radial interconnected distributed power networks. The proposed approach combines the advantages of both the genetic algorithm (GA) and sequential quadratic programming (SQP) methods to optimize the objective function of relay coordination in the best manner. Thus, the proposed hybrid techniques improved the convergence of the problem and increased the likelihood of obtaining a globally optimal solution. Finally, to validate the effectiveness of the proposed algorithm, it was tested through three case studies involving the IEEE 3-Bus, 8-Bus, and modified 30-Bus distribution networks. In addition, the results were compared to those obtained using previous methods. The results obtained from the comparison of the proposed method and recent advanced research indicate that the proposed optimization approach is preeminent in terms of accuracy and total operating time as well as the continuity of the minimum margin time requirements between the primary/backup relay pairs.

An algorithm for solving the equilibrium points of high-dimensional nonlinear vehicle dynamic system based on a combination of genetic algorithm, sequential quadratic programming method, and continuation method

The paper proposes an algorithm that combines Genetic Algorithm, Sequential Quadratic Programming, and Continuation Method to solve the equilibrium points of a multi-degree-of-freedom vehicle nonlinear system. The algorithm’s effectiveness is demonstrated by applying it to search for equilibrium points of a 5-degree-of-freedom (5DOF) nonlinear vehicle model, which considers both longitudinal and lateral motion. The dynamic equilibrium points of front-wheel-drive, rear-wheel-drive, and all-wheel-drive vehicles with different front-wheel steering angle inputs are calculated. Taking the front-wheel-drive system as an example, the system equilibrium points are further analyzed using phase space analysis and eigenvalue analysis for verification. In addition, the impact of the driving effect on the equilibrium points bifurcation is investigated. The results show that compared with the Genetic Algorithm alone and the combination method of Genetic Algorithm and Sequential Quadratic Programming, the proposed algorithm can effectively and accurately solve the equilibrium points of the 5DOF vehicle model. The study also reveals that the driving effect significantly influences the vehicle equilibrium point bifurcation.

A Hybrid Genetic Algorithm-Based Parameter Identification Method for Nonlinear Hysteretic System with Experimental Verification

The Bouc–Wen nonlinear hysteretic model is widely used in nonlinear systems, and it is difficult to identify the parameters of Bouc–Wen model because of its high nonlinearity. In the paper, a hybrid genetic algorithm combined with sequential quadratic programming is proposed to solve the problem about the parameter identification of Bouc–Wen model. Sequential quadratic programming method has good local convergence and superlinear convergence rate. Therefore, compared with the genetic algorithm, the proposed identification method can accelerate the convergence speed in parameter recognition of Bouc–Wen model and achieve excellent recognition accuracy. Through the function test and the numerical simulation of the shear structure, it is proved that the proposed method has high convergence speed and accurate identification. In addition, the theory and method proposed in this paper are combined with Bouc–Wen model to identify parameters of overall restoring force model of the energy-dissipation structures, the identification results are in good agreement with the experimental results, verifying reliability and accuracy of the model and robustness of the proposed identification method.