In this study, we propose a landing guidance control method for the Moon using two control methods. The landing of a spacecraft on the Moon is divided into two phases: the powered descending phase and the vertical des...
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In this study, we propose a landing guidance control method for the Moon using two control methods. The landing of a spacecraft on the Moon is divided into two phases: the powered descending phase and the vertical descending phase. The powered descending phase aims to optimize the entire trajectory to satisfy the termination constraint, instead of allowing for a relatively long control period. This phase performs feedback control using trajectory updates via nonlinear optimization. The vertical-descending phase aims to achieve accurate control over a short control period. This phase applies nonlinear model predictive control for fast optimization on finite time intervals. First, the landing of a spacecraft on the Moon is modeled as a two- body problem of the Moon and spacecraft, and equations of motion are derived. Subsequently, we formulated an optimization problem for each phase and developed the proposed landing guidance method by combining the two control methods. Furthermore, numerical simulations based on the derived equations of motion were performed to confirm the effectiveness of the proposed method and to compare its performance with another optimization method, the successive convexification (SCvx) algorithm.
This paper aims to optimize steel moment frames within a performance-based design framework by implementing a neural network-integrated metaheuristic algorithm. Performance-based optimization of steel structures poses...
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Mobile edge computing, a prospective wireless communication framework, can contribute to offload a large number of tasks to unmanned aerial vehicle (UAV) mobile edge servers. Besides, the demand for server computation...
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The nonlinear optimization problem with possible infeasible constraints was studied early by Burke (J Math Anal Appl, 139:19-351, 1989) and was revisited by Dai and Zhang (CSIAM Trans Appl Math, 2:551-584, 2021;Math P...
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The nonlinear optimization problem with possible infeasible constraints was studied early by Burke (J Math Anal Appl, 139:19-351, 1989) and was revisited by Dai and Zhang (CSIAM Trans Appl Math, 2:551-584, 2021;Math Program, 200:633-667, 2023) in a broad perspective. This paper considers nonlinear optimization with least & ell;1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document}-norm measure of constraint violations and introduces the concepts of the D-stationary point, the DL-stationary point, and the DZ-stationary point with the help of exact penalty function. If the stationary point is feasible, they correspond to the Fritz-John stationary point, the KKT stationary point, and the singular stationary point, respectively. In order to show the usefulness of these specific stationary points, we propose an exact penalty sequential quadratic programming (SQP) method with inner and outer iterations and analyze its global and local convergence. The proposed method admits convergence to a D-stationary point and rapid infeasibility detection without driving the penalty parameter to zero, which demonstrates the commentary given in Byrd et al (SIAM J Optim, 20:2281-2299, 2010) and can be thought to be a supplement of the theory of nonlinear optimization on rapid detection of infeasibility. Some illustrative examples and preliminary numerical results demonstrate that the proposed method is robust and efficient in solving infeasible nonlinear problems and a degenerate problem without LICQ in the literature.
We discuss the (first- and second-order) optimality conditions for nonlinear programming under the relaxed constant rank constraint qualification (RCRCQ). Although the optimality conditions are well established in the...
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We discuss the (first- and second-order) optimality conditions for nonlinear programming under the relaxed constant rank constraint qualification (RCRCQ). Although the optimality conditions are well established in the literature, the proofs presented here are based solely on the well-known inverse function theorem. This is the only prerequisite from real analysis used to establish two auxiliary results needed to prove the optimality conditions. To be precise, we provide a simple and alternative proof that RCRCQ is a constraint qualification that implies strong second-order optimality conditions.
Transmission network expansion planning is a critical and complex problem related to the operation and development of electrical power systems. It is typically formulated as a mixed-integer nonlinear programming (MINL...
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Transmission network expansion planning is a critical and complex problem related to the operation and development of electrical power systems. It is typically formulated as a mixed-integer nonlinear programming (MINLP) problem with combinatorial characteristics. Various mathematical models have been proposed to better approximate real-world system behavior, but even the most relaxed formulations remain computationally challenging. This paper introduces a search space reduction strategy to reduce the gap between the optimal solution of the MINLP model and its relaxed counterpart by strategically considering surrogate constraints. This approach enhances computational efficiency, significantly reducing processing time when using an optimization solver. By applying this method, we successfully determined the previously unknown optimal solution for the Brazilian north-northeast system.
In the smooth constrained optimization setting, this work introduces the Domain Complementary Approximate Karush-Kuhn-Tucker (DCAKKT) condition, inspired by a sequential optimality condition recently devised for non-s...
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In the smooth constrained optimization setting, this work introduces the Domain Complementary Approximate Karush-Kuhn-Tucker (DCAKKT) condition, inspired by a sequential optimality condition recently devised for non-smooth constrained optimization problems. It is shown that the augmented Lagrangian method can generate limit points satisfying DCAKKT, and it is proved that such a condition is not related to previously established sequential optimality conditions. An essential characteristic of the DCAKKT is to capture the asymptotic potential increasing of the Lagrange multipliers using a single parameter. Besides that, DCAKKT points satisfy the Strong Approximate Gradient Projection (SAGP) condition. Due to the intrinsic features of DCAKKT, which combine strength and generality, this novel and genuine sequential optimality condition may shed some light upon the practical performance of algorithms that are yet to be devised.
DC microgrids are becoming more common in modern systems, so computation methodologies such as the power flow, the optimal power flow, and the state estimation require being adapted to this new reality. This paper dea...
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DC microgrids are becoming more common in modern systems, so computation methodologies such as the power flow, the optimal power flow, and the state estimation require being adapted to this new reality. This paper deals with the latter problem, which consists of reconstructing the state variables given voltage and power measurements. Although the model of DC grids is undoubtedly less complicated than its counterpart AC, it is still a nonlinear/non-convex optimization problem. Our approach is based on the idea of solving the problem in a matrix space. Although it may be counter-intuitive to transform from R-n to R-nxn, a matrix space exhibits better geometric properties that allow an elegant formulation and, in some cases, an efficient form to solve the optimization problem. We compare two methodologies: semidefinite programming and manifold optimization. The former relaxes the problem to a convex set, whereas the latter maintains the geometry of the original problem. A specialized gradient method is proposed to solve the problem in the matrix manifold. Extensive numerical experiments are conducted to showcase the key characteristics of both methodologies. Our study aims to shed light on the potential benefits of employing matrix space techniques in addressing operation problems in DC microgrids and power system computations in general.
The loss of octane in the gasoline refining process can cause huge economic losses. However, the analysis and optimisation of octane loss is a high-dimensional nonlinear programming problem. In this work, we propose a...
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The loss of octane in the gasoline refining process can cause huge economic losses. However, the analysis and optimisation of octane loss is a high-dimensional nonlinear programming problem. In this work, we propose a compound variable selection scheme. Based on the results of independent variables by outlier and high correlation filtering, the representative operations are selected by random forest and grey correlation analysis, and the octane loss is then predicted by the BP neural network and XGBoost. To optimise the octane loss, an operation optimisation scheme based on fast gradient modification (FGM) is proposed. Experiments show that the composite variable selection scheme proposed in this paper can effectively screen independent and representative variables and has high prediction accuracy for octane loss. The proposed optimisation method also has sufficient feasibility and meets the needs of real scenes.
This study proposes a versatile and efficient optimisation method for discrete coils that induce a magnetic field by their steady currents. The prime target is gradient coils for MRI (Magnetic Resonance Imaging). The ...
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This study proposes a versatile and efficient optimisation method for discrete coils that induce a magnetic field by their steady currents. The prime target is gradient coils for MRI (Magnetic Resonance Imaging). The derivative (gradient) of the z-component the magnetic field, which is calculated by the Biot-Savart's law, with respect to the z-coordinate in the Cartesian xyz coordinate system is considered as the objective function. Then, the derivative of the objective function with respect to a change of coils in shape is formulated according to the concept of shape optimisation. The resulting shape derivative (as well as the Biot-Savart's law) is smoothly discretised with the closed B-spline curves. In this case, the control points (CPs) of the curves are naturally selected as the design variables. As a consequence, the shape derivative is discretised to the sensitivities of the objective function with respect to the CPs. Those sensitivities are available to solve the present shape-optimisation problem with a certain gradient-based nonlinear-programming solver. The numerical examples exhibit the mathematical reliability, computational efficiency, and engineering applicability of the proposed methodology based on the shape derivative/sensitivities and the closed B-spline curves.
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