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

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.

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.

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.

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.

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.

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.

Recently, nonlinear programming solvers have been used to solve a range of mathematical programs with equilibrium constraints (MPECs). In particular, sequential quadratic programming (SQP) methods have been very successful. This paper examines the local convergence properties of SQP methods applied to MPECs. SQP is shown to converge superlinearly under reasonable assumptions near a strongly stationary point. A number of examples are presented that show that some of the assumptions are difficult to relax.

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.

A smoothing Newton-type method for generalized nonlinear complementarity problem

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.

Identification of fractional order non– homogeneous Hammerstein-Wiener MISO continuous systems

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

In this paper, we propose a multi-beam model for antenna array pattern synthesis (AAPS) problem. The model uses a conic trust region algorithm (CTRA) similarly proposed in this paper to optimize its cost function. Undoubtedly, whole algorithm e-ciency ultimately lies on the CTRA, thereof, we propose a method to improve the iterative algorithm's e-ciency. Unlike traditional trust region methods that resolve sub-problems, the CTRA e-ciently searches a region via solving a inequation, by which it identifles new iteration points when a trial step is rejected. Thus, the proposed algorithm improves computational e-ciency. Moreover, the CTRA has strong convergence properties with the local superlinear and quadratic convergence rate under mild conditions, and exhibits high e-ciency and robustness. Finally, we apply the combinative algorithm to AAPS. Numerical results show that the method is highly robust, and computer simulations indicate that the algorithm excellently performs AAPS problem.