Numerical optimization of texture shape for parallel surfaces under unidirectional and bidirectional sliding

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%.

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

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

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.

Time-varying digital filters are widely used in dynamic signal processing applications, but their transient response can significantly impact performance, particularly in real-time systems. This study focuses on reducing transient time in time-varying filters through second-order section (SOS) optimization. By employing a numerical optimization approach, we selectively adjust the coefficients of a single SOS within a higher-order filter to minimize the transient period while maintaining overall stability. Using a sequential quadratic programming (SQP) algorithm, we determine a time-varying coefficient trajectory over a finite horizon, ensuring a rapid convergence to steady-state behavior. Experimental results demonstrate that this targeted coefficient adaptation reduces transient time by up to 80% compared to conventional static designs, with minimal computational overhead. Additionally, a comparative analysis with traditional linear time-invariant (LTI) filters highlights the advantage of this method in suppressing transient oscillations while preserving long-term filter characteristics. The proposed approach provides a practical and efficient strategy for enhancing filter responsiveness in applications requiring both stability and real-time adaptability. These findings suggest that selective time variation in SOS decomposition can be a valuable tool in digital filter design, improving efficiency without excessive memory or processing demands.

This paper presents design and optimization of a new ‘star-like’ texture shape with an aim to improve the tribological performance. Initial studies showed that the triangle effect is the most dominant in reducing the friction. Motivated with the triangle effect, a ‘star-like’ texture shape consisting of a series of triangular spikes around the centre of the texture is proposed. It is hypothesized that by increasing the triangular effect on a texture shape, the converging micro-wedge effect is expected to increase, hence increasing the film pressure and reducing the friction. Using the well-known Reynolds equation, numerical modelling of surface texturing is implemented via finite difference method. Simulation results showed that the number of apex points of the new ‘star-like’ texture has a significant effect on the film pressure and the friction coefficient. A 6-pointed texture at a texture density of 0.4 is shown to be the optimum shape. The new optimum star-like texture reduces the friction coefficient by 80%, 64.39%, 19.32% and 16.14%, as compared to ellipse, chevron, triangle and circle, respectively. This indicates the potential benefit of the proposed new shape in further enhancing the hydrodynamic lubrication performance of slider bearing contacts.

We present in this paper a novel method (called PID design through numerical optimization) for the design of adaptive fuzzy PID controllers to achieve optimal control performance. By applying the numerical optimization, the fuzzy PID design problem is transferred to a numerical optimization problem. First, a fuzzy parameter tuner is built to generate initial PID parameters, including positions and shapes of fuzzy membership functions and scaling factors. Then the gradient-based Sequential Quadratic programming (SQP) algorithm is employed to iteratively minimize the cost function by iterating the parameters. Unlike conventional PID design, this method is capable of reaching the desired control performance, such as minimum overshoot or long term stability. Another unique feature is that the optimized adaptive PID controller is applicable to a wide variety of time-varying and nonlinear systems. The proposed method is applied to the induction motor control problem and the experimental results are presented to demonstrate its effectiveness and performance.

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.

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.

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.

A flexible joint model and the corresponding mechanism synthesis approach are proposed in this article for simultaneously optimizing the topology and dimension configuration of planar mechanisms. The proposed approach leverages topology optimization, enabling the generation of diverse configurations without any predetermined baseline mechanism. The flexible joint model proposed in this article consists of a revolute joint and two orthogonal prismatic joints, which represent the relative motions of the adjacent rigid bodies in three degrees of freedom (DOF). The zero-length springs are employed to restrict the relative motion DOF, thereby emulating the functionality of different joint types. The flexible joint model allows for the configuration of the mechanism to be expressed using only a few parameters. The synthesis problem of the path-generating mechanism is converted into a numerical parameter optimization problem based on the strain energy of the flexible joint model and solved by the sequential quadratic programming (SQP) algorithm. To address inaccuracies in the calculation of degrees of freedom in the Grübler–Kutzbach (G–K) formulation, a supplementary constraint function based on the strain energy of the flexible joint is proposed. To demonstrate the validity of the proposed approach, several mechanism synthesis problems are solved by this approach.

Most of the published work on trust region algorithms for constrained optimization is derived from the original work of Fletcher on trust region algorithms for nondifferentiable exact penalty functions. These methods are restricted to applications where a reasonable estimate of the magnitude of an optimal Kuhn–Tucker multiplier vector can be given. More recently an effort has been made to extend the trust region methodology to the sequential quadratic programming (SQP) algorithm of Wilson, Han, and Powell. All of these extensions to the Wilson–Han–Powell SQP algorithm consider only the equality-constrained case and require strong global regularity hypotheses. This paper presents a general framework for trust region algorithms for constrained problems that does not require such regularity hypotheses and allows very general constraints. The approach is modeled on the one given by Powell for convex composite optimization problems and is driven by linear subproblems that yield viable estimates for the value of an exact penalty parameter. These results are applied to the Wilson–Han–Powell SQP algorithm and Fletcher’s $S\ell_1 QP$ algorithm. Local convergence results are also given.