Sequential Quadratic Programming Method Research Articles

ALESQP: An Augmented Lagrangian Equality-Constrained SQP Method for Optimization with General Constraints

We present a new algorithm for infinite-dimensional optimization with general constraints, called ALESQP. In short, ALESQP is an augmented Lagrangian method that penalizes inequality constraints and solves equality-constrained nonlinear optimization subproblems at every iteration. The subproblems are solved using a matrix-free trust-region sequential quadratic programming (SQP) method that takes advantage of iterative, i.e., inexact linear solvers, and is suitable for large-scale applications. A key feature of ALESQP is a constraint decomposition strategy that allows it to exploit problem-specific variable scalings and inner products. We analyze convergence of ALESQP under different assumptions. We show that strong accumulation points are stationary. Consequently, in finite dimensions ALESQP converges to a stationary point. In infinite dimensions we establish that weak accumulation points are feasible in many practical situations. Under additional assumptions we show that weak accumulation points are stationary. We present several infinite-dimensional examples where ALESQP shows remarkable discretization-independent performance in all of its iterative components, requiring a modest number of iterations to meet constraint tolerances at the level of machine precision. Also, we demonstrate a fully matrix-free solution of an infinite-dimensional problem with nonlinear inequality constraints.

Оптимизация сжатых деревянных стоек переменного сечения по критерию максимума критической нагрузки

The article presents a numerical and analytical solution to the problem of optimizing compressed rods according to the criterion of the maximum critical load with a possible loss of stability in two planes. We consider a wooden bar of rectangular cross section, the height of which varies according to a linear law, and the width is constant. The calculation is performed in an elastic formulation. A constraint on the constancy of the rod mass is introduced. Variable parameters are the ratio of the minimum section height to the maximum, as well as the ratio of the section width to the maximum height. Numerical search for the optimal solution is performed in the MATLAB environment using the method of sequential quadratic programming. It has been established that the use of rods with a cross-sectional height that varies linearly along the length is effective only if the rod is fixed in at least one of the planes according to the “pinched-free end” scheme. It has been established that the increase in the critical load when using rods with a linearly varying cross-sectional height can be up to 22%.

An effective nonlinear interval sequential quadratic programming method for uncertain inverse problems

An effective nonlinear interval sequential quadratic programming method is proposed to provide an efficient tool for uncertain inverse problems. Assisted by the ideology of sequential quadratic programming and dimension-reduction analysis theory, the interval inverse problem is transformed into several interval arithmetic and deterministic optimizations, which could enhance computational efficiency without losing much accuracy. The novelty of the proposed method lies in two main aspects. First, an alternate updating strategy is proposed to identify the radii and midpoints of the interval inputs in each cycle, which could reduce the number of iterative steps. Second, the standard quadratic models are constructed based on the dimension-reduction analysis results, rather than the second-order Taylor expansion. Therefore, the interval arithmetic can be applied to efficiently calculate the interval response, which avoids the inner optimization. Moreover, a novel iterative mechanism is developed to accelerate the convergence rate of the proposed method. Finally, two numerical examples and an engineering application are adopted to verify its feasibility, accuracy and efficiency.

A Stabilized Sequential Quadratic Programming Method for Optimization Problems in Function Spaces

In this paper, we propose a stabilized sequential quadratic programming (SQP) method for optimization problems in function spaces. A form of the problem considered in this paper can widely formulate many types of applications, such as obstacle problems, optimal control problems, and so on. Moreover, the proposed method is based on the existing stabilized SQP method and can find a point satisfying the Karush-Kuhn-Tucker (KKT) or asymptotic KKT conditions. One of the remarkable points is that we prove its global convergence to such a point under some assumptions without any constraint qualifications. In addition, we guarantee that an arbitrary accumulation point generated by the proposed method satisfies the KKT conditions under several additional assumptions. Finally, we report some numerical experiments to examine the effectiveness of the proposed method.

Analysis of single and multi-objective optimization of the pultrusion process

This work used a computational strategy to optimize a pultrusion process. Based on mass and energy balance equations, the mathematical model was implemented into Ansys CFX® and Matlab® tools. A pultrusion die with six heaters and C-section composite geometry was used as a studied case. For the single objective optimization, the sum of the heaters' temperatures was considered as objective function with a minimum degree of cure of 0.9 imposed as a constraint. Particle swarm optimization (PSO) and sequential quadratic programming (SQP) algorithms were considered for single objective optimization. The results indicated that the SQP method could reduce the objective function and computational cost by 1.58% and 30.31%, respectively, concerning the PSO algorithm. However, the results also indicated that the performance of the SQP is highly dependent on the initial temperature estimates. The PSO and NSGA-II algorithms were applied to solve the multi-objective optimization in which pull speed maximization and minimization of heaters' temperatures were defined as objective functions. Results indicated that NSGA-II was 18.8% faster than the PSO strategy. The Pareto curve of the two methods presented a similar profile, evidencing that a higher pull speed requires greater energy consumption. Finally, the results show that the Pareto curve is helpful for predicting the set of resulting optimal points, which also makes it possible to detect unfeasible combinations of temperature and pull speed values.

A modified sequential quadratic programming method for sparse signal recovery problems

We propose a modified sequential quadratic programming method for solving the sparse signal recovery problem. We start by going through the well-known smoothed-ℓ0 technique and provide a smooth approximation of the objective function. Then, a variant of the sequential quadratic programming method equipped with a new approach for solving subproblems is proposed. We investigate the global convergence of the method in detail. In comparison to several well-known algorithms, simulation results demonstrate the promising performance of the proposed method.

Sequential quadratic programming-based non-cooperative target distributed hybrid processing optimization method

The distributed hybrid processing optimization problem of non-cooperative targets is an important research direction for future networked air-defense and anti-missile firepower systems. In this paper, the air-defense anti-missile targets defense problem is abstracted as a nonconvex constrained combinatorial optimization problem with the optimization objective of maximizing the degree of contribution of the processing scheme to non-cooperative targets, and the constraints mainly consider geographical conditions and anti-missile equipment resources. The grid discretization concept is used to partition the defense area into network nodes, and the overall defense strategy scheme is described as a nonlinear programming problem to solve the minimum defense cost within the maximum defense capability of the defense system network. In the solution of the minimum defense cost problem, the processing scheme, equipment coverage capability, constraints and node cost requirements are characterized, then a nonlinear mathematical model of the non-cooperative target distributed hybrid processing optimization problem is established, and a local optimal solution based on the sequential quadratic programming algorithm is constructed, and the optimal firepower processing scheme is given by using the sequential quadratic programming method containing non-convex quadratic equations and inequality constraints. Finally, the effectiveness of the proposed method is verified by simulation examples.

An SQP-based multiple shooting algorithm for large-scale PDE-constrained optimal control problems

Multiple shooting methods for solving optimal control problems have been developed rapidly in the past decades and are widely considered a promising direction to speed up the optimization process. Here we propose and analyze a new multiple shooting algorithm based on a sequential quadratic programming (SQP) method that is suitable for optimal control problems governed by large-scale time-dependent partial-differential equations (PDEs). We investigate the structure of the KKT matrix and solve the large-scale KKT system by a preconditioned conjugate gradient algorithm. A simplified block Schur complement preconditioner is proposed, that allows for the parallelization of the method in the time domain. The proposed algorithm is first validated for an optimal control problem constrained by the Nagumo equation. The results indicate that considerable accelerations can be achieved for multiple shooting approaches with appropriate starting guesses and scaling of the matching conditions. We further apply the proposed algorithm to a two-dimensional velocity tracking problem governed by the Navier–Stokes equations. We find algorithmic speed-ups of up to 12 versus single shooting on up to 50 shooting windows. We also compare results with earlier work that uses an augmented Lagrangian algorithm instead of SQP, showing better performance of the SQP method for most of the cases.

An Enhanced Multioperator Runge–Kutta Algorithm for Optimizing Complex Water Engineering Problems

Water engineering problems are typically nonlinear, multivariable, and multimodal optimization problems. Accurate water engineering problem optimization helps predict these systems’ performance. This paper proposes a novel optimization algorithm named enhanced multioperator Runge–Kutta optimization (EMRUN) to accurately solve different types of water engineering problems. The EMRUN’s novelty is focused mainly on enhancing the exploration stage, utilizing the Runge–Kutta search mechanism (RK-SM), the covariance matrix adaptation evolution strategy (CMA-ES) techniques, and improving the exploitation stage by using the enhanced solution quality (IESQ) and sequential quadratic programming (SQP) methods. In addition to that, adaptive parameters were included to improve the stability of these two stages. The superior performance of EMRUN is initially tested against a set of CEC-17 benchmark functions. Afterward, the proposed algorithm extracts parameters from an eight-parameter Muskingum model. Finally, the EMRUM is applied to a practical hydropower multireservoir system. The experimental findings show that EMRUN performs much better than advanced optimization approaches. Furthermore, the EMRUN has demonstrated the ability to converge up to 99.99% of the global solution. According to the findings, the suggested method is a competitive algorithm that should be considered in optimizing water engineering problems.

A thrust allocation strategy for intelligent ships based on model prediction control

In order to solve the problem of the traditional sequential quadratic programming thrust allocation method, such as limited feasible region and low propulsion efficiency, a thrust allocation strategy based on model predictive control is proposed in this paper. The proposed thrust allocation strategy is realized by rolling optimization of model predictive control, and moreover, considering the possibility of thruster failure, a fault-tolerant thrust allocation strategy is proposed. The simulation results show that the proposed strategy can not only make the ship run in the expected condition but also reduce the average power consumption by 16.3% compared with the traditional sequential quadratic programming method and has good fault tolerance in the face of thruster failure.

A revised sequential quadratic semidefinite programming method for nonlinear semidefinite optimization

In 2020, Yamakawa and Okuno proposed a stabilized sequential quadratic semidefinite programming (SQSDP) method for solving, in particular, degenerate nonlinear semidefinite optimization problems. The algorithm is shown to converge globally without a constraint qualification, and it has some nice properties, including the feasible subproblems, and their possible inexact computations. In particular, the convergence was established for approximate-Karush-Kuhn-Tucker (AKKT) and trace-AKKT conditions, which are two sequential optimality conditions for the nonlinear conic contexts. However, recently, complementarity-AKKT (CAKKT) conditions were also considered, as an alternative to the previous mentioned ones, that is more practical. Since few methods are shown to converge to CAKKT points, at least in conic optimization, and to complete the study associated to the SQSDP, here we propose a revised version of the method, maintaining the good properties. We modify the previous algorithm, prove the global convergence in the sense of CAKKT, and show some preliminary numerical experiments.

Optimal synthesis of a planar mechanism using Matlab: Example of slider crank in a rowing motion

<abstract> <p>This paper illustrates the conducted effort to introduce the methodology of optimal synthesis of mechanisms through an engineering problem under Matlab. This project is part of a first course on poly-articulated mechanisms and robotics at the graduate level. The course combines both the theoretical and implementation under Matlab aspects to achieve its goals. The example of the rowing machine is considered to introduce the crank-slider mechanism and the kinematic analysis using complex numbers. The mechanism is associated with a spring to ensure the device simulating the resistance in the rowing bench simulator. The optimal synthesis problem is formulated for the desired effort to perform and solved using the Sequential Quadratic Programming method. All developments are implemented under Matlab.</p> </abstract>

Multi-User Dynamic Computation Offloading and Resource Allocation in 5G MEC Heterogeneous Networks with Static and Dynamic Subchannels

With the rapid development of Mobile Edge Computing (MEC) technology, the computationally intensive requests of end devices can be offloaded to MEC servers directly, which equipped at the edge of wireless networks. Through offloading, the performances such as the execution delay as well as the energy consumption can be effectively improved, which can significantly enhance the quality of user experience. Given the dynamics and randomness of computation requests arrival, the energy in the battery, the radio network environment, and the computation resource in the MEC server, it is a challenge to perform efficient offloading. Based on these problems, this paper proposes dynamic optimization schemes with queuing theory for the cases of the static subchannel and dynamic subchannel during a time slot separately in 5G MEC heterogeneous networks with multiple MDs equipped with the function of energy harvesting. In the schemes, offloading decisions and radio allocation strategies will be dynamically coordinated. They are also jointly allocated along with changing wireless communication resources and computation demands aiming to minimize the system average execution delay. Specifically, it is assumed that the offloading requests can be transmitted through either macro base stations or small base stations. In the case of the static subchannel, a joint resource allocation and computation offloading scheme based on Lyapunov optimization and Simulated Annealing Genetic Algorithm (SAGA) is put forward. As for the dynamic subchannel, the master-and-slave model is adopted and solved by SAGA and Sequential Quadratic Programming (SQP) method. At last, the effectiveness of the proposed schemes is verified through several simulations.

A variant of the united multi-operator evolutionary algorithms using sequential quadratic programming and improved SHADE-cnEpSin

United multi-operator evolutionary algorithms (UMOEAs) combine multi-operator differential evolution (DE), the multi-operator genetic algorithm (MOGA), and the covariance matrix adaption evolution strategy (CMA-ES). UMOEAs-II, an improved version of UMOEAs, uses three differential evolution variants as multi-operator differential evolution (MODE), and CMA-ES. In this study, we further reform UMOEAs-II using an improved SHADE-cnEpSin that employs a novel adaptive strategy of scaling factor F, a crossover rate cri,j updating mechanism which can calculate crossover rate for the ith individual with a particular jth component, an improved rank-based selective pressure based mutation strategy, and nonlinear population size reduction along with sequential quadratic programming method. The effectiveness of the improved rank-based selective pressure based mutation strategy, nonlinear population size reduction, and sequential quadratic programming are evident from the individual validations. The novel framework, enhanced the exploration and exploitation abilities, is named UMOEAs-III and is evaluated using the CEC2017 benchmark functions. The experiments are tested on 10, 30, 50, and 100 dimensions. The experimental results demonstrate the outstanding performance of UMOEAs-III in both low and high-dimensional tests compared to the state-of-the-art DE-based variants and hybrid algorithms.

A Novel Model Predictive Control Based Co-Optimization Strategy for Velocity Planning and Energy Management of Intelligent PHEVs

Facilitated by the advanced abilities in environment sensing and integrated communication, intelligent plug-in hybrid electric vehicles (IPHEVs) enable massive autonomy in decision-making. The evolution towards intelligence imposes stringent demand on optimal control in IPHEVs, of which the velocity planning and energy management is strongly coupled. To address this issue, a novel model predictive control (MPC) based control strategy is designed for IPHEV with the dramatically improved ability in real time implementation. The inexact Kantorovich sequential quadratic programming (iKSQP) method is exploited to efficiently solve the cooperative control problem within the receding horizon. The reference velocity involving the detailed description on future driving and careful consideration of safe distance to forward vehicles is obtained via the microcosmic traffic flow analysis (MTFA). The simulation results manifest the superior performance of the raised optimal control strategy in cooperatively planning optimal velocity and managing power allocation in real time.

Comparison of algorithms for multi-objective optimization of radio technical device characteristics

Objectives. The selection of a method for solving multi-objective optimization problems has many practical applications in diverse fields. The present work compares the results of applying different methods to the selected classes of problems by solution quality, time consumption, and various other criteria.Methods. Five problems related to the multi-objective optimization of analog and digital filters, as well as multistep impedance-matching microwave transformers, are considered. One of the compared algorithms comprises the Third Evolution Step of Generalized Differential Evolution (GDE3) population-based algorithm for searching the full approximation of the Pareto set simultaneously, while the other three algorithms minimize the scalar objective function to find only one element of the Pareto set in a single search cycle: these comprise Multistart Pattern Search (MSPS), Multistart Sequential Quadratic Programming (MSSQP) method and Particle Swarm Optimization (PSO) algorithms.Results. The computer experiments demonstrated the capability of GDE3 to solve all considered problems. MSPS and PSO showed significantly inferior results than to GDE3 for two problems. In one problem, MSSQP could not be used to reach acceptable decisions. In the other problems, MSPS, MSSQP, and PSO reached decisions comparable with GDE3. The time consumption of the MSPS and PSO algorithms was much greater than that of GDE3 and MSSQP.Conclusions. The GDE3 algorithm may be recommended as a basic method for solving the considered problems. Algorithms minimizing scalar objective function may be used to obtain several elements of the Pareto set. It is necessary to investigate the impact of landscape features of individual quality indices and scalar objective functions on the extreme search process.

Dynamic Analysis and Path Planning of a Turtle-Inspired Amphibious Spherical Robot.

A dynamic path-planning algorithm based on a general constrained optimization problem (GCOP) model and a sequential quadratic programming (SQP) method with sensor input is proposed in this paper. In an unknown underwater space, the turtle-inspired amphibious spherical robot (ASR) can realise the path-planning control movement and achieve collision avoidance. Due to the special underwater environments, thrusters and diamond parallel legs (DPLs) are installed in the lower hemisphere to realise accurate motion control. A propulsion model for a novel water-jet thruster based on experimental analysis and a modified Denavit-Hartenberg (MDH) algorithm are developed for multiple degrees of freedom (MDOF) to realize high-precision and high-speed motion control. Simulations and experiments verify that the effectiveness of the GCOP and SQP algorithms can realize reasonable path planning and make it possible to improve the flexibility of underwater movement with a small estimation error.

Anchor Chain Optimization Design of a Catenary Anchor Leg Mooring System Based on Adaptive Sampling

A catenary anchor leg mooring system (CALM) is one of the main kinds of offshore transport terminals. Its buoyancy is connected by multiple anchor chains fixed on the seabed. Because a large deformation characterizes the anchor chain, it is prone to fatigue failure under dynamic loads in marine environments. These factors lead to many challenges in the design optimization of anchor chains. This study aims to develop a rapid optimization design framework for a mooring anchor chain with cost minimization as the design objective. In this framework, an approximation model of the mooring analysis is built based on an adaptive sampling method, and a combination of a genetic algorithm and a sequential quadratic programming method is utilized to optimize the established approximation model. The results show that the framework significantly reduces the computation time, and the error of the final optimization result obtained by adaptive sampling is significantly reduced. We found that using a quadratic or elliptic function as an adaptive function is good enough to obtain the optimization result.

A split Bregman method solving optimal reactive power dispatch for a doubly-fed induction generator-based wind farm

This paper proposes an optimal reactive power control method to maximize wind farm revenue and minimize the total electrical losses of a doubly-fed induction generator (DFIG)-based wind farm. Specifically, the split Bregman method is used to solve the optimal control problem in a distributed manner. That is, the optimization problem is decomposed into sub-problems by the optimal distributed control strategy, and each sub-problem is solved independently in each local controller through the parallel method, which reduces the calculating burden and improves the information privacy. Thus, when a fault occurs, the proposed distributed control strategy can overcome the system fault and improve the reliability and security of the system. Furthermore, an economic financial model of annual revenue is contributed to examine the income impact with or without certified emission reduction (CER) by the clean development mechanism (CDM). Compared with the dual ascent (DA) method, sequential quadratic programming (SQP) method and the proportional dispatch method (PDM), the annual revenue (AR) of the wind farm using the proposed split Bregman method is the highest. Simulation results demonstrate that this method has promising performance in both optimization quality and computational efficiency.

Life-Cycle Production Optimization of the CO2-Water-Alternating-Gas Injection Process Using Least-Squares Support-Vector Regression Proxy

SummaryIn this study, we present a framework for efficient estimation of the optimal carbon dioxide (CO2)-water-alternating-gas (WAG) parameters for robust production-optimization problems by replacing a high-fidelity model with a least-squares support-vector regression (LS-SVR) model. We provide insight and information on the proper selection of feature space and training samples of the LS-SVR proxy model for the CO2-WAG life cycle production optimization problem. Given a set of training points generated from high-fidelity model-based simulation results, an LS-SVR-based proxy model is built to approximate a reservoir-simulation model. The estimated optimal design parameters are then found by maximizing net present value (NPV) using the LS-SVR proxy as the forward model within an iterative-sampling-refinement (ISR) optimization algorithm that is designed specifically to promote the accuracy of the proxy model for robust production optimization. As an optimization tool, the sequential quadratic programming (SQP) method is used. CO2-WAG design variables are CO2 injection and water injection rates for each injection well at each cycle, production bottomhole pressure (BHP) for each production well at each WAG half-cycle, and inflow control valve (ICV) for each well at each WAG half-cycle and at each valve. We study different scenarios where we fix some of the design variables to investigate the importance of design variables on the life cycle production optimization of the CO2-WAG problem. We compare the performance of the proposed method using the LS-SVR runs with the popular stochastic simplex approximate gradient (StoSAG) and reservoir simulation runs for a synthetic example considering a three-layer, channelized reservoir with four injectors and nine producers. Results show that with the properly selected feature space and training points, the proposed LS-SVR-based ISR optimization framework is at least 1.5–8 times computationally more efficient, depending on the cases considered, than the StoSAG using a high-fidelity numerical simulator. However, we observe that the size and sampling of the training data, as well as the selection of well controls and their bound constraints for the well controls, seem to be influential on the performance of the LS-SVR-based optimization method. This is the first LS-SVR application to the CO2-WAG optimal well-control problem. The proposed LS-SVR-based ISR optimization framework has the potential to be used as an efficient tool for the CO2-WAG optimization problem.