Optimal attitude and flight vector recovery for large transport aircraft using sequential quadratic programming

Direct optimal control methods first discretize a continuous-time Optimal Control Problem (OCP) and then solve the resulting Nonlinear Program (NLP). Sequential Quadratic Programming (SQP) is a popular family of algorithms to solve this finite dimensional optimization problem. In the specific case of a least squares cost, the Generalized Gauss-Newton (GGN) method is a popular approach which works very well under some assumptions. This paper proposes a Sequential Convex Quadratic Programming (SCQP) scheme which exploits additional convexities in the NLP in order to generalize the GGN algorithm, possibly extend its applicability and improve its local convergence. These properties are studied in detail for the proposed SCQP algorithm, which will be compared to the classical GGN method using a numerical case study of the optimal control of an inverted pendulum.

Future wireless systems must be designed to meet high data rates and a variety of services such as voice, video, etc. which consume more energy. Therefore, designing energy-efficient systems in recent years has become an inevitable trend. In this paper energy efficient resource allocation in orthogonal frequency division multiple access (OFDMA) systems is discussed. After formulating the resource allocation problem, maximizing-energy efficiency (EE)-lower-bound-based downlink subcarrier assignment (MDSA) algorithm is used to solve the problem that allocates subcarrier and power recursively. In this algorithm, first primary subcarriers are assigned to users and then power is allocated and this process continues recursively until all subcarriers are assigned to the users. Power allocation is done by the use of proposed sequential Quadratic programming (SQP) method. Then, simulation results are compared with bisection based power adaptation (BPA) algorithm method which has different power allocation. Results show that power allocation by SQP method has higher energy efficiency. Moreover, SQP shows higher convergence rate in solving the problem (finding the answer) in comparison to BPA method with less simulation time.

In this paper, we propose a robust sequential quadratic programming (SQP) method for nonlinear programming without using any explicit penalty function and filter. The method embeds the modified QP subproblem proposed by Burke and Han (Math Program 43:277---303, 1989) for the search direction, which overcomes the common difficulty in the traditional SQP methods, namely the inconsistency of the quadratic programming subproblems. A non-monotonic technique is employed further in a framework in which the trial point is accepted whenever there is a sufficient relaxed reduction of the objective function or the constraint violation function. A forcing sequence possibly tending to zero is introduced to control the constraint violation dynamically, which is able to prevent the constraint violation from over-relaxing and plays a crucial role in global convergence and the local fast convergence as well. We prove that the method converges globally without the Mangasarian---Fromovitz constraint qualification (MFCQ). In particular, we show that any feasible limit point that satisfies the relaxed constant positive linear dependence constraint qualification is also a Karush---Kuhn---Tucker point. Under the strict MFCQ and the second order sufficient condition, furthermore, we establish the superlinear convergence. Preliminary numerical results show the efficiency of our method.

In this paper, the design of non-uniform concentric circular antenna arrays (CCAAs) of isotropic radiators with optimum side lobe level reduction is presented. The newly-proposed global evolutionary optimization methods; namely: the biogeography based optimization (BBO) is used to determine a set of weights that provides a radiation pattern with optimum side lobe level reduction with the constraint of a fixed major lobe beamwidth. The results obtained from BBO are compared with those obtained using the Matlab function Fmincon which uses a sequential quadratic programming (SQP) method. The comparison shows that the design of non-uniformly excited CCAAs using SQP method provides a side lobe level reduction that is better than that obtained using global stochastic optimization methods, indicating that global optimization techniques are not really needed in this problem.

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

Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be computationally nonviable. This paper presents a second derivative SQP method based on quadratic subproblems that are either convex, and thus may be solved efficiently, or need not be solved globally. Additionally, an explicit descent-constraint is imposed on certain QP subproblems, which “guides” the iterates through areas in which nonconvexity is a concern. Global convergence of the resulting algorithm is established.

Optimizations of a photoresist coating process for photolithography in wafer manufacture via a radial basis neural network: A case study

In this paper, a new algorithm, namely, a reduced Hessian sequential quadratic programming (SQP) method, for solving electromagnetic inverse problems is proposed. The electromagnetic inverse problem is considered to be a constrained nonlinear programming. The reduced Hessian SQP method finds the solution of this constrained nonlinear programming by solving a sequential of quadratic programming subproblems. The reduced Hessian scheme is applied to reduce the requirement of computational memory of the basic SQP method for large inverse problems. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method, and some comparisons show that the proposed method has a better convergence and a faster speed than the previous methods.

This study analyzed contour distortions, wear and tensile properties of polypropylene (PP) components applied in the interior coffer of automobiles. A hybrid method integrating a trained generalized regression neural network (GRNN) and a sequential quadratic programming (SQP) method is proposed to determine an optimal parameter setting of the injection‐molding process. The specimens were prepared under different injection‐molding conditions by changing melting temperatures, injection speeds, and injection pressures. Average contour distortions at six critical locations, wear and tensile properties were selected as the quality targets. Sixteen experimental runs, based on a Taguchi orthogonal array table, were utilized to train the GRNN and then the SQP method was applied to search for an optimal setting. The trained GRNN was capable of predicting average contour distortions, wear and tensile properties at various injection‐molding conditions. In addition, the analysis of variance (ANOVA) was implemented to identify significant factors for the molding process and the proposed algorithm was compared with traditional schemes like the Taguchi method and the design of experiments (DOE) approach. Copyright © 2007 John Wiley & Sons, Ltd.

We consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We assume for the objective that its evaluation, gradient, and Hessian are inaccessible, while one can compute their stochastic estimates by, for example, subsampling. We propose a stochastic algorithm based on sequential quadratic programming (SQP) that uses a differentiable exact augmented Lagrangian as the merit function. To motivate our algorithm design, we first revisit and simplify an old SQP method Lucidi (J. Optim. Theory Appl. 67(2): 227–245, 1990) developed for solving deterministic problems, which serves as the skeleton of our stochastic algorithm. Based on the simplified deterministic algorithm, we then propose a non-adaptive SQP for dealing with stochastic objective, where the gradient and Hessian are replaced by stochastic estimates but the stepsizes are deterministic and prespecified. Finally, we incorporate a recent stochastic line search procedure Paquette and Scheinberg (SIAM J. Optim. 30(1): 349–376 2020) into the non-adaptive stochastic SQP to adaptively select the random stepsizes, which leads to an adaptive stochastic SQP. The global “almost sure” convergence for both non-adaptive and adaptive SQP methods is established. Numerical experiments on nonlinear problems in CUTEst test set demonstrate the superiority of the adaptive algorithm.

We have already briefly touched nonlinear programming in the last two chapters, in which we introduced the multiple shooting discretized optimal control problem, a Nonlinear Program (NLP), and presented the outer convexification and relaxation approach that allows to compute approximations to local Mixed–Integer Optimal Control Problem (MIOCP) solutions by solving a reformulated and discretized but possibly much larger Optimal Control Problem (OCP). This chapter is concerned with theory and numerical methods for the solution of NLPs and equips the reader with definitions and algorithms required for the following chapters of this thesis. We present optimality conditions characterizing locally optimal solutions and introduce Sequential Quadratic Programming (SQP) methods for the iterative solution of NLPs. The evaluation of the matching condition constraints of the discretized optimal control problem requires the solution of Initial Value Problems (IVPs). To this end, we present one step methods for non–stiff Ordinary Differential Equations (ODEs) and discuss the efficient and consistent computation of sensitivities of IVPs solutions. The familiar reader may wish to continue with chapter 4 rightaway, and refer back to this chapter should the need arise.KeywordsSequential Quadratic ProgrammingActive ConstraintAutomatic DifferentiationDiscretization GridStrict ComplementarityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Optimal load clipping with time of use rates

Varying-Radius Tunnel-Following NMPC for Robot Manipulators Using Sequential Convex Quadratic Programming

The problem of calculating gradients for discretized optimal control problems is addressed. These gradients are needed by a sequential quadratic programming (SQP) method, which is used to solve the discretized optimal control problem. Two approaches for gradient calculation are discussed and compared numerically. The first approach uses sensitivity equations, the second uses adjoint equations. It turns out that it depends on the problem dimensions which approach is more preferable compared to the other. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Sequential Quadratic Programming (SQP) denotes an established class of methods for solving nonlinear optimization problems via an iterative sequence of Quadratic Programs (QPs). Several approaches in the literature have established local and global convergence of the method. This paper considers a variant to SQP that, instead of solving each QP, at each iteration follows one gradient step along a direction that is proven to be a descent direction for an augmented Lagrangian of the nonlinear problem, and in turn is used to generate the next QP. We prove global convergence to a critical point of the original nonlinear problem via a line search that requires the same assumptions as the SQP method. The method is then applied to nonlinear Model Predictive Control (MPC). To simplify the problem formulation and achieve faster convergence, we propose a locally convergent reformulation. An important speed-up is observed in practice via a specific initialization. The computational efficiency of the proposed method is finally shown in a numerical example.