This paper presents a convex programming algorithm based on modified Rodrigues parameters for a six-degree-of-freedom asteroid powered landing trajectory design problem. The trajectory design problem is formulated as ...
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This paper presents a convex programming algorithm based on modified Rodrigues parameters for a six-degree-of-freedom asteroid powered landing trajectory design problem. The trajectory design problem is formulated as a nonconvex fuel-optimal control problem with nonlinear coupled translational and rotational dynamics, nonconvex state and control constraints. In order to tackle the fuel-optimal control problem in the convexification framework, the original nonconvex continuous-time optimization problem is converted into a convex discrete-time optimization subproblem by linearizing and discretizing the dynamics and constraints. The effect of the coupling of translational and rotational dynamics on the convexification of nonconvex control constraints is discussed. The successive convexification method of solving a sequence of constrained convex subproblem is used to generate the optimal trajectory. The validity of the proposed algorithm for generating fuel-optimal trajectories and the effect of asteroid gravity on generated trajectories are examined through simulations of landing on different irregular asteroids. The Monte Carlo simulation is performed to examine the calculation performance of the proposed algorithm comparing to the Radau pseudospectral method algorithm and the proposed algorithm with the rotational motion parameterized by quaternions.
In this paper, we study the optimization problem (PWE) of minimizing a convex function over the set of weakly efficient solutions of a convex multiobjective problem. This is done by using the fact that each lower semi...
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In this paper, we study the optimization problem (PWE) of minimizing a convex function over the set of weakly efficient solutions of a convex multiobjective problem. This is done by using the fact that each lower semicontinuous convex function is an upper envelope of its affine minorants together with a generalized cutting plane method. We give necessary conditions for optimal solutions of the problem (PWE). Moreover, a novel algorithm for solving the problem (PWE) together with numerical results are presented. We also prove that the proposed algorithm terminates after a finite numbers of iterations, and the algorithm is coded in MATLAB language and evaluated by numerical examples.
A study proposes a learning-based and theory-supported optimal control method (LB&TS OCM) for fuel-optimal powered descent. It demonstrates applying supervised learning (SL) directly to find the optimal solution, ...
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A study proposes a learning-based and theory-supported optimal control method (LB&TS OCM) for fuel-optimal powered descent. It demonstrates applying supervised learning (SL) directly to find the optimal solution, the learning process is guided by the necessary conditions derived from the Pontryagin’s minimum principle. The combination of SL methods and fundamentals of optimal control theory dramatically reduces the dimension of the learning space by exploiting the features of the optimal solution. Based on Hamiltonian and first-order necessary conditions, the optimal solution of the fuel-optimal powered descent guidance (FOPDG) problem is represented by a few critical parameters. Therefore, instead of learning all state and control variables, the proposed approach only needs to learn the identified critical parameters.
nonlinear programming has found useful applications in protein biophysics to help understand the microscopic exchange kinetics of data obtained using hydrogen-deuterium exchange mass spectrometry (HDX-MS). Finding a m...
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nonlinear programming has found useful applications in protein biophysics to help understand the microscopic exchange kinetics of data obtained using hydrogen-deuterium exchange mass spectrometry (HDX-MS). Finding a microscopic kinetic solution for HDX-MS data provides a window into local protein stability and energetics allowing them to be quantified and understood. Optimization of HDX-MS data is a significant challenge, however, due to the requirement to solve a large number of variables simultaneously with exceptionally large variable bounds. Modeled rates are frequently uncertain with an explicate dependency on the initial guess values. In order to enhance the search for a minimum solution in HDX-MS optimization, the ability of selected constrained variables to propagate throughout the data is considered. We reveal that locally bound constrained optimization induces a global effect on all variables. The global response to local constraints is large and surprisingly long-range, but the outcome is unpredictable, unexpectedly decreasing the overall accuracy of certain data sets depending on the stringency of the constraints. Utilizing previously described in-house validation criteria based on covariance matrices, a method is described that is able to accurately determine whether constraints benefit or impair the optimization of HDX-MS data. From this, we establish a new two-stage method for our online optimizer HDXmodeller that can effectively leverage locally bound variables to enhance HDX-MS data modeling.
In this paper, we propose two trust-region algorithms for unconstrained optimization. The trust-region algorithms minimize a model of the objective function within the trust-region, next update the size of the region ...
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In this paper, we propose two trust-region algorithms for unconstrained optimization. The trust-region algorithms minimize a model of the objective function within the trust-region, next update the size of the region and then repeat the procedure to find a first-order stationary point for the objective function. The size of the trust-region at each step is very critical to the effectiveness of the algorithm, particularly for large-scale problems, because minimizing the model at each step needs the gradient and the Hessian information of the objective function. Our modified trust-region algorithms are opportunistic in the sense that they explore beyond the trust-region if the boundary of the region prevents the algorithm from accepting a more beneficial point. It occurs when there is a very good agreement between the model and the objective function on the trust-region boundary, and we can find a step outside the trust-region with smaller value of the model while at which the agreement between the model and the objective function remains good. We show that the algorithms are convergent. Initial numerical experiments show that the proposed algorithms are more efficient than the traditional trust-region algorithm for a large majority of problems in the CUTEst suite.
In this work, movable antenna (MA) is invoked for enhancing the task completion performance of a mobile edge computing (MEC) system. Specifically, in the considered system model, a base station equipped with MAs assis...
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The range of multirotor Unmanned Aerial Vehicle (UAV) applications has grown significantly over the last decade. This is to be attributed to their simple mechanical design, along with hovering and maneuvering capabili...
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In recent years, the Internet of Medical Things (IoMT) has significantly boosted the healthcare industry. Federated learning (FL) can enhance the utilization of patient data while protecting privacy. Despite the great...
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In this paper, we examine coexistence of enhanced mobile broadband (eMBB) and ultra-reliable low-latency communication (URLLC) services within an intelligent reconfigurable surface (IRS)-assisted terahertz multi-cell ...
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In viral marketing campaigns, incentivized consumers can act as sales agents by sharing information. In this study, we investigate the problem of incentive rate determination over a network of consumers to maximize th...
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In viral marketing campaigns, incentivized consumers can act as sales agents by sharing information. In this study, we investigate the problem of incentive rate determination over a network of consumers to maximize the profit of a single good by a monopolist. For this purpose, we develop an epidemic spreading model to explore the dynamics of a viral marketing campaign under network externalities and incentivized individuals. We will examine two cases of homogeneous and heterogeneous incentive rates. In each case, we derive an N-intertwined dynamics model and obtain the existence and stability conditions of a trade-free or an endemic equilibrium. By treating the incentive as a control parameter, we investigate the problem of maximizing the monopolist's profit by formulating two nonlinear programming models. In the case of homogeneous incentive rates, results show that the optimal incentive is determined by devising a balance between the consumers' states in the Markov process. In the heterogeneous case, it is observed that despite the existence of a strong correlation with different centrality measures, the optimal incentive allocation cannot be solely determined by centrality measures. (C) 2020 Elsevier B.V. All rights reserved.
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