A Robust Trust Region Method for Constrained Nonlinear Programming Problems

This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm proposed by Fukushima et al. [Computational Optimization and Applications, 10 (1998), 5-34], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration, one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size. Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence. Some preliminary numerical results are reported.

Multidisciplinary design optimization (MDO) was performed on a helicopter rotor blade. The blade was modeled as a rigid flapping blade for dynamics; Blade Element Theory (BET) was the analysis approach to model the aerodynamic loading, and a simple linearly elastic hollowed rectangular section was the main structural component. MATLAB was used to solve the flapping differential equations and its Sequential Quadratic Programming (SQP) and Genetic Algorithm (GA) were used for the optimization. A Particle Swarm Optimization (PSO) routine was also tested. The optimization process consisted of three cases. The first case was a simple cantilever beam under centrifugal and an assumed bending loads. The optimization was performed using the SQP, GA, and PSO algorithms. The SQP resulted in the superior design with 75.45 compared to the GA's 87.1 and the PSO's 79.2, but a local minimum was present. The second case was an expansion of the first case by turning it into multidisciplinary problem. Aerodynamics was included in the design variables and objective function. Only the SQP algorithm was used and there was a reduction in hub vertical shear by 33.6%. The blade mass increased by 36.84%. The last case was an improvement to the second by creating a multiobjective problem by including the hub radial shear and the results were improved significantly by reducing the hub vertical shear by 34.06% and radial shear by 17.87% with a reduction of blade mass by 23.86%.

Optimal Design of Heat Exchanger Networks by Using SQP Algorithm Based on GPU Acceleration

Recently, with the wide adoption of electric vehicles, transportation network has shown different characteristics and been further developed. In this paper, we present a new time-flow impedance function, which may be more realistic than the existing time-flow impedance functions. Based on this new impedance function, we present an optimization model for a mixed-mode traffic network in which battery electric vehicles (BEVs) and gasoline vehicles (GVs) are chosen. We suggest two approaches to handle the model: One is to use the interior point (IP) algorithm and the other is to employ the sequential quadratic programming (SQP) algorithm. Three numerical examples are presented to illustrate the efficiency of these approaches. In particular, our numerical results show that more travelers prefer to choosing BEVs when the distance limit of BEVs is long enough and the unit operating cost of GVs is higher than that of BEVs, and the SQP algorithm is faster than the IP algorithm.

Performance analysis of support vector machine, Gaussian Process Regression, sequential quadratic programming algorithms in modeling hydrogen-rich syngas production from catalyzed co-gasification of biomass wastes from oil palm

Comparison of SQP and AL algorithms for deterministic constrained production optimization of hydrocarbon reservoirs

ABSTRACTThe rapid growth of interconnected devices and data traffic necessitates robust mobile networks, especially in rural areas with unreliable grid power. This paper introduces an optimisation framework for the off‐grid green open radio access network architecture utilising renewable energy to meet this demand. The framework aims to optimise power and bandwidth allocation, ensuring high data rates and reliability from sustainable sources. In addition, the CO2 emission factor and the quality of service are also optimised in which several assumptions and network metrics have been incorporated such as power consumption (PC), load demand, number of virtual machines (VMs) and maintenance cost. The problem is formulated as the weighted nonlinear problem. First, the model has been formulated using simplified data rate assumption and has been solved mathematically using Lagrange multipliers. Subsequently, the mathematical problem has been solved using the gradient descent numerical solution and then compared with sequential quadratic programming (SQP) and interior point algorithms. The second assumption is formulated as the data rate considering the noise and interference factors; the comparative analysis of SQP, active set and interior point algorithms has been presented. The third case assumed the dynamic behaviour of the network of users and VMs, where the problem is also solved mathematically and numerically. Empirical evidence from rural deployments confirms the enhancement of mobile coverage and service provision through the integration of solar and wind‐powered base stations.

The present work proposes a methodology for optimization of a liquefied biomethane (LBM) production plant. The LBM production plant comprises amine-based absorption upgrading followed by a single expander refrigeration cycle. The processes were modeled using Aspen HYSYS® and optimized through a Sequential Quadratic Programming algorithm. Any changes in the operating conditions of the upgrading process will affect the cooling demand in the liquefaction, while the opposite is not true. Based on this, a sequential optimization approach starting with the upgrading process is proposed. In order to accommodate the connection between the processes, different objective functions were formulated for the sequential optimization approach. The results from the sequential approach were compared with an overall optimization approach, where the entire LBM plant was optimized simultaneously. The results indicate that the same solution was obtained both for the sequential approach and the simultaneous approach. For the sequential approach, however, the best result was observed when the interaction between the upgrading and liquefaction processes was accounted for by considering the effect of the upgrading process on the exergy requirement in the liquefaction process.

When applying the sequential quadratic programming (SQP) algorithm to topology optimization, using the quasi-Newton methods or calculating the Hessian matrix directly will result in a considerable amount of calculation, making it computationally infeasible when the number of optimization variables is large. To solve the above problems, this paper creatively proposes a method for calculating the approximate Hessian matrix for structural topology optimization with minimum compliance problems. Then, the second-order Taylor expansion transforms the original problem into a series of separable and easy-to-solve convex quadratic programming (QP) subproblems. Finally, the quadratic programming optimality criteria (QPOC) method and the QP solver of MATLAB are used to solve the subproblems. Compared with other sequential quadratic programming methods, the advantage of the proposed method is that the Hessian matrix is diagonally positive definite and its calculation is simple. Numerical experiments on an MBB beam and cantilever beam verify the feasibility and efficiency of the proposed method.

With the development of wireless communication, higher requirements arise for train-ground wireless communications in high-speed railway (HSR) scenarios. The millimeter-wave (mm-wave) frequency band with rich spectrum resources can provide users in HSR scenarios with high performance broadband multimedia services, while the full-duplex (FD) technology has become mature. In this paper,we study train-ground communication system performance in HSR scenarios with mobile relays (MRs) mounted on rooftop of train and operating in the FD mode. We formulate a nonlinear programming problem to maximize network capacity by allocation of spectrum resources. Then, we develop a sequential quadratic programming (SQP) algorithm based on the Lagrange function to solve the bandwidth allocation optimization problem fortrack-side base station (BS) and MRs in this mm-wave train-ground communication system. Extensive simulation results demonstrate that the proposed SQP algorithm can effectively achieve high network capacity for train-ground communication in HSR scenarios while being robust to the residual self-interference (SI).

In this paper, a family of trust-region interior-point sequential quadratic programming (SQP) algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise, e.g., from the discretization of optimal control problems. The algorithms treat states and controls as independent variables. They are designed to take advantage of the structure of the problem. In particular they do not rely on matrix factorizations of the linearized constraints but use solutions of the linearized state equation and the adjoint equation. They are well suited for large scale problems arising from optimal control problems governed by partial differential equations. The algorithms keep strict feasibility with respect to the bound constraints by using an affine scaling method proposed, for a different class of problems, by Coleman and Li [SIAM J. Optim., 6 (1996), pp. 418--445] and they exploit trust-region techniques for equality-constrained optimization. Thus, they allow the computation of the steps using a variety of methods, including many iterative techniques. Global convergence of these algorithms to a first-order Karush--Kuhn--Tucker (KKT) limit point is proved under very mild conditions on the trial steps. Under reasonable, but more stringent, conditions on the quadratic model and on the trial steps, the sequence of iterates generated by the algorithms is shown to have a limit point satisfying the second-order necessary KKT conditions. The local rate of convergence to a nondegenerate strict local minimizer is q-quadratic. The results given here include, as special cases, current results for only equality constraints and for only simple bounds. Numerical results for the solution of an optimal control problem governed by a nonlinear heat equation are reported.

The sequential quadratic programming and genetic algorithms are finely tuned on the optimal design of a brushless DC wheel motor. Combining both methods, a hybrid approach is tested. Multiobjective optimizations are performed using Nondominated Sorting Genetic Algorithm, Strength Pareto Evolutionary Algorithm, and a variable weighted sum of objectives with the sequential quadratic programming. The Pareto fronts are compared in term of accuracy, uniformity, and coverage criteria using some quality indicators.

We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizes of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is not assumed that the iterates lie on a compact set.

For current sequential quadratic programming (SQP) type algorithms, there exist two problems: (i) in order to obtain a search direction, one must solve one or more quadratic programming subproblems per iteration, and the computation amount of this algorithm is very large. So they are not suitable for the large-scale problems; (ii) the SQP algorithms require that the related quadratic programming subproblems be solvable per iteration, but it is difficult to be satisfied. By using e-active set procedure with a special penalty function as the merit function, a new algorithm of sequential systems of linear equations for general nonlinear optimization problems with arbitrary initial point is presented. This new algorithm only needs to solve three systems of linear equations having the same coefficient matrix per iteration, and has global convergence and local superlinear convergence. To some extent, the new algorithm can overcome the shortcomings of the SQP algorithms mentioned above.

Sequential Quadratic Programming (SQP) for optimal control in direct numerical simulation of turbulent flow