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IEEE Symposium on Computers and Communications (ISCC)

作者： Xavier, Daniel M. Silva, Natassya B. F. Branco, Kalinka R. L. J. C. Univ Sao Paulo Escola Engn Sao Carlos Sao Carlos Brazil Univ Tecnol Fed Parana Cornejo Procopio Brazil Univ Sao Paulo Inst Ciencias Matemat & Comp Sao Carlos Brazil

ISBN: (纸本)9781728129990

Unmanned Aerial Vehicles (UAVs) are aircraft that can be autonomously operated and doesn't need a pilot aboard. Consequently, the autopilot is one of the main parts of an UAV, being responsible for stabilising the aircraft during the flight, executing navigation tasks and sensing the environment. Several path-following simulations for loiter paths are described in the literature, but most of them only consider the kinematics model of an aircraft. Therefore, this paper compares path-following algorithms for loiter paths in a more realistic scenario, using Software-in-the-Loop simulations and considering the dynamic model of the aircraft in the flight simulator X-Plane. The algorithms compared are: Carrot-Chasing, Pure Pursuit and Line-of-Sight (PLOS) and Non-Linear Guidance Law (NLGL). Lastly, a new algorithm (NLGL+) is proposed with a modification from the original algorithm and its results show smaller errors and less effort than all path-following algorithms.

关键词： Software-in-the-loop unmanned aerial vehicles navigation path-following algorithms

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3D path-following algorithms for Unmanned Aerial Vehicles Adjusted with Genetic Algorithm 1

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4th Workshop on Communication in Critical Embedded Systems (WoCCES)

作者： Pelizer, Guilherme, V Silva, Natassya B. F. Branco, Kalinka R. L. J. C. Univ Sao Paulo Ave Trabalhador Sao Carlense 400 BR-13566590 Sao Carlos SP Brazil

ISBN: (数字)9783319614038

ISBN: (纸本)9783319614038;9783319614021

Unmanned Aerial Vehicle (UAV) is a growing research topic due to its wide range of applications. One of its major challenges is the development of the autopilot, responsible for keeping the aircraft in desired flight conditions and for executing navigation tasks. A navigation task that is usually necessary is the path-following, which guarantees that the aircraft follows a predefined trajectory. It is possible to find several approaches for this function, based in geometric and control techniques;however, compared only for the 2D scenario. Therefore, this paper objective is to present new extended path-following algorithms for the 3D scenario, based in the well-known path-following algorithms Lookahead, Non-Linear Guidance Law (NLGL), Pure Pursuit and Line-of-Sight (PLOS) and Vector Field. The algorithms parameters are obtained with Genetic Algorithm optimisation and a comparison between all of them is performed in an environment with and without wind. The results from the simulations show that Vector Field has the best performance and PLOS has the worse one due to a high effort demanded.

关键词： path-following algorithms Genetic Algorithm Unmanned Aerial Vehicles

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An algorithmic view of ℓ2 regularization and some path-following algorithms

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2021年第1期22卷 6123-6184页

作者： Yunzhang Zhu Renxiong Liu Department of Statistics The Ohio State University Columbus OH

We establish an equivalence between the ℓ2-regularized solution path for a convex loss function, and the solution of an ordinary differentiable equation (ODE). Importantly, this equivalence reveals that the solution path can be viewed as the flow of a hybrid of gradient descent and Newton method applying to the empirical loss, which is similar to a widely used optimization technique called trust region method. This provides an interesting algorithmic view of ℓ2 regularization, and is in contrast to the conventional view that the ℓ2 regularization solution path is similar to the gradient flow of the empirical loss. New path-following algorithms based on homotopy methods and numerical ODE solvers are proposed to numerically approximate the solution path. In particular, we consider respectively Newton method and gradient descent method as the basis algorithm for the homotopy method, and establish their approximation error rates over the solution path. Importantly, our theory suggests novel schemes to choose grid points that guarantee an arbitrarily small suboptimality for the solution path. In terms of computational cost, we prove that in order to achieve an ε-suboptimality for the entire solution path, the number of Newton steps required for the Newton method is O(ε-1/2), while the number of gradient steps required for the gradient descent method is O(ε-1 ln(ε-1)). Finally, we use ℓ2-regularized logistic regression as an illustrating example to demonstrate the effectiveness of the proposed path-following algorithms.

关键词： ℓ2 regularization path-following algorithms Newton method gradient descent method convergence rate analysis

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path-following METHODS FOR LINEAR-PROGRAMMING

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SIAM REVIEW 1992年第2期34卷 167-224页

作者： GONZAGA, CC Federal Univ of Rio de Janeiro Rio de Janeiro Braz

In this paper a unified treatment of algorithms is described for linear programming methods based on the central path. This path is a curve along which the cost decreases, and that stays always far from the boundary of the feasible set. Several parameterizations of this curve are described in primal and primal-dual problems, and it is shown how different algorithms are obtained by following the curve using different parameterizations. Polynomial algorithms are obtained by following the curve approximately, and this concept becomes precise by using explicit rules for measuring the proximity of a point in relation to the central path.

关键词： LINEAR PROGRAMMING INTERIOR POINT METHODS path-following algorithms

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A new path-following algorithm for nonlinear P*complementarity problems

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2006年第2期34卷 183-214页

作者： Zhao, Y. B. Li, D. Chinese Acad Sci AMSS Inst Appl Math Beijing 100080 Peoples R China Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China

Based on the recent theoretical results of Zhao and Li [Math. Oper. Res., 26 (2001), pp. 119-146], we present in this paper a new path-following method for nonlinear P* complementarity problems. Different from most existing interior-point algorithms that are based on the central path, this algorithm tracks the "regularized central path" which exists for any continuous P* problem. It turns out that the algorithm is globally convergent for any P* problem provided that its solution set is nonempty. By different choices of the parameters in the algorithm, the iterative sequence can approach to different types of points of the solution set. Moreover, local superlinear convergence of this algorithm can also be achieved under certain conditions.

关键词： nonlinear complementarity problems path-following algorithms regularized central path Tikhonov regularization P*-mappings

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Superlinear convergence of interior-point algorithms for semidefinite programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1998年第1期99卷 103-119页

作者： Potra, FA Sheng, R Univ Iowa Dept Math Iowa City IA 52242 USA Argonne Natl Lab Div Math & Comp Sci Argonne IL 60439 USA

We prove the superlinear convergence of the primal-dual infeasible interior-point path-following algorithm proposed recently by Kojima, Shida, and Shindoh and by the present authors, under two conditions: (i) the semidefinite programming problem has a strictly complementary solution;(ii) the size of the central path neighborhood approaches zero. The nondegeneracy condition suggested by Kojima, Shida, and Shindoh is not used in our analysis. Our result implies that the modified algorithm of Kojima, Shida, and Shindoh, which enforces condition (ii) by using additional corrector steps, has superlinear convergence under the standard assumption of strict complementarity. Finally, we point out that condition (ii) can be made weaker and show the superlinear convergence under the strict complementarity assumption and a weaker condition than (ii).

关键词： semidefinite programming path-following algorithms infeasible interior-point algorithms polynomiality superlinear convergence

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Joint Power Allocation and Beamforming for Energy-Efficient Two-Way Multi-Relay Communications

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2017年第10期16卷 6660-6671页

作者： Sheng, Zhichao Tuan, Hoang Duong Duong, Trung Q. Poor, H. Vincent Univ Technol Sydney Fac Engn & Informat Technol Ultimo NSW 2007 Australia Queens Univ Belfast Belfast BT7 1NN Antrim North Ireland Princeton Univ Dept Elect Engn Princeton NJ 08544 USA

This paper considers the joint design of user power allocation and relay beamforming in relaying communications, in which multiple pairs of single-antenna users exchange information with each other via multiple-antenna relays in two time slots. All users transmit their signals to the relays in the first time slot while the relays broadcast the beamformed signals to all users in the second time slot. The aim is to maximize the system's energy efficiency (EE) subject to quality-of-service (QoS) constraints in terms of exchange throughput requirements. The QoS constraints are nonconvex with many nonlinear cross-terms, so finding a feasible point is already computationally challenging. The sum throughput appears in the numerator while the total consumption power appears in the denominator of the EE objective function. The former is a nonconcave function and the latter is a nonconvex function, making fractional programming useless for EE optimization. Nevertheless, efficient iterations of low complexity to obtain its optimized solutions are developed. The performance of the multiple-user and multiple-relay networks under various scenarios is evaluated to show the merit of the proposed method.

关键词： Two-way relaying information exchange (IE) energy efficiency (EE) quality-of-service (QoS) relay beam-forming power allocation joint optimization path-following algorithms

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Beamforming Optimization for Physical Layer Security in MISO Wireless Networks

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2018年第14期66卷 3710-3723页

作者： Sheng, Zhichao Hoang Duong Tuan Duong, Trung Q. Poor, H. Vincent Univ Technol Sydney Sch Elect & Data Engn Sydney NSW 2007 Australia Queens Univ Belfast Belfast BT7 1NN Antrim North Ireland Princeton Univ Dept Elect Engn Princeton NJ 08544 USA

A wireless network of multiple transmitter-user pairs overheard by an eavesdropper, where the transmitters are equippedwith multiple antennas, while the users and eavesdropper are equipped with a single antenna, is considered. At different levels of wireless channel knowledge, the problem of interest is beamforming to optimize the users' quality-of-service (QoS) in terms of their secrecy throughputs or maximize the network's energy efficiency under users' QoS. All these problems are seen as very difficult optimization problems with many nonconvex constraints and nonlinear equality constraints in beamforming vectors. The paper develops path-following computational procedures of low complexity and rapid convergence for the optimal beamforming solution. Their practicability is demonstrated through numerical examples.

关键词： Multi-input single-output network secure communication energy-efficient communication beamforming path-following algorithms

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Self-scaled barriers and interior-point methods for convex programming

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MATHEMATICS OF OPERATIONS RESEARCH 1997年第1期22卷 1-42页

作者： Nesterov, YE Todd, MJ CORNELL UNIV SCH OPERAT RES & IND ENGNITHACANY 14853 CORNELL CTR APPL MATH ITHACANY

This paper provides a theoretical foundation for efficient interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are self-scaled. For such problems we devise long-step and symmetric primal-dual methods. Because of the special properties of these cones and barriers, our algorithms can take steps that go typically a large fraction of the way to the boundary of the feasible region, rather than being confined to a ball of unit radius in the local norm defined by the Hessian of the barrier.

关键词： convex programming conical form interior point algorithms self-concordant barrier self-scaled cone self-scaled barrier path-following algorithms potential-reduction algorithms

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Infinite-dimensional quadratic optimization: Interior-point methods and control applications

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APPLIED MATHEMATICS AND OPTIMIZATION 1997年第1期36卷 43-66页

作者： Faybusovich, L Moore, JB RES SCH INFORM SCI & ENGN DEPT SYST ENGN CANBERRA ACT 0200 AUSTRALIA RES SCH INFORM SCI & ENGN COOPERAT RES CTR ROBUST & ADAPT SYST CANBERRA ACT 0200 AUSTRALIA

An infinite-dimensional convex optimization problem with the linear-quadratic cost function and linear-quadratic constraints is considered, We generalize the interior-point techniques of Nesterov-Nemirovsky to this infinite-dimensional situation. The complexity estimates obtained are similar to finite-dimensional ones. We apply our results to the linear-quadratic control problem with quadratic constraints. It is shown that for this problem the Newton step is basically reduced to the standard LQ problem.

关键词： control problems quadratic constraints path-following algorithms

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