A quadratically constrained quadratic programming problem is considered in a Hilbert space setting, where neither the objective nor the constraint are convex functions. Necessary and sufficient conditions are provided...
详细信息
A quadratically constrained quadratic programming problem is considered in a Hilbert space setting, where neither the objective nor the constraint are convex functions. Necessary and sufficient conditions are provided to guarantee that the problem admits solutions for every initial data (in an adequate set).
In this work we present some exactness conditions for the Shor relaxation of diagonal (or, more generally, diagonalizable) QCQPs, which extend the conditions introduced in different recent papers about the same topic....
详细信息
In this work we present some exactness conditions for the Shor relaxation of diagonal (or, more generally, diagonalizable) QCQPs, which extend the conditions introduced in different recent papers about the same topic. It is shown that the Shor relaxation is equivalent to two convex quadratic relaxations. Then, sufficient conditions for the exactness of the relaxations are derived from their KKT systems. It will be shown that, in some cases, by this derivation previous conditions in the literature, which can be viewed as dual conditions, since they only involve the Lagrange multipliers appearing in the KKT systems, can be extended to primal-dual conditions, which also involve the primal variables appearing in the KKT systems.
Vision-based control of mobile robots in formation has received a lot of attention. Real-time and efficient control is crucial for practical applications. An efficient model predictive control method is proposed using...
详细信息
ISBN:
(纸本)9798350366907;9789887581581
Vision-based control of mobile robots in formation has received a lot of attention. Real-time and efficient control is crucial for practical applications. An efficient model predictive control method is proposed using a recurrent neural network (RNN)-based optimizer to obtain optimal solutions in real-time. First, an efficient and robust model predictive control method is introduced for vision-based mobile robot formation control with stability constraints. Second, an RNN solver that decomposes the QCQP problem into a series of subproblems for solving is proposed. Finally, the applicability and performance of the proposed control scheme are demonstrated by typical hardware experiments.
This article studies the problem of real-time relative pose estimation of multi-UAV systems based on inter-UAV distance measurement and onboard odometry. In large-scale UAV systems, the centralized localization proble...
详细信息
ISBN:
(纸本)9798350366907;9789887581581
This article studies the problem of real-time relative pose estimation of multi-UAV systems based on inter-UAV distance measurement and onboard odometry. In large-scale UAV systems, the centralized localization problem using only distance measurements is challenging from the perspective of computational burden. The concerned relative pose estimation problem is formulated as a squared distance weighted least squares problem and is then decomposed to be executed on each UAV. Constraints on the relative poses of neighboring UAVs with mutual distance measurements are added to the problem under the condition that some UAVs lack direct distance measurements, subsequently transforming it into a quadratically constrained quadratic programming (QCQP) form for solving. Simulation experiments show that the proposed optimization problem is effective in real-time relative pose estimation of large-scale UAVs with distance measurements and odometry, and can yield more accurate pose estimates than the relevant literature.
It has been recently shown that an additional therapeutic gain may be achieved if a radiotherapy plan is altered over the treatment course using a new treatment paradigm referred to in the literature as spatiotemporal...
详细信息
It has been recently shown that an additional therapeutic gain may be achieved if a radiotherapy plan is altered over the treatment course using a new treatment paradigm referred to in the literature as spatiotemporal fractionation. Because of the nonconvex and large-scale nature of the corresponding treatment plan optimization problem, the extent of the potential therapeutic gain that may be achieved from spatiotemporal fractionation has been investigated using stylized cancer cases to circumvent the arising computational challenges. This research aims at developing scalable optimization methods to obtain high-quality spatiotemporally fractionated plans with optimality bounds for clinical cancer cases. In particular, the treatment-planning problem is formulated as a quadraticallyconstrainedquadratic program and is solved to local optimality using a constraint-generation approach, in which each subproblem is solved using sequential linear/quadraticprogramming methods. To obtain optimality bounds, cutting-plane and column-generation methods are combined to solve the Lagrangian relaxation of the formulation. The performance of the developed methods are tested on deidentified clinical liver and prostate cancer cases. Results show that the proposed method is capable of achieving local-optimal spatiotemporally fractionated plans with an optimality gap of around 10%-12% for cancer cases tested in this study. Summary of Contribution: The design of spatiotemporally fractionated radiotherapy plans for clinical cancer cases gives rise to a class of nonconvex and large-scale quadratically constrained quadratic programming (QCQP) problems, the solution of which requires the development of efficient models and solution methods. To address the computational challenges posed by the large-scale and nonconvex nature of the problem, we employ large-scale optimization techniques to develop scalable solution methods that find local-optimal solutions along with optimality bounds. We
quadraticallyconstrainedquadratic programs (QCQPs) are a fundamental class of optimization problems well-known to be NP-hard in general. In this paper we study conditions under which the standard semidefinite progra...
详细信息
quadraticallyconstrainedquadratic programs (QCQPs) are a fundamental class of optimization problems well-known to be NP-hard in general. In this paper we study conditions under which the standard semidefinite program (SDP) relaxation of a QCQP is tight. We begin by outlining a general framework for proving such sufficient conditions. Then using this framework, we show that the SDP relaxation is tight whenever the quadratic eigenvalue multiplicity, a parameter capturing the amount of symmetry present in a given problem, is large enough. We present similar sufficient conditions under which the projected epigraph of the SDP gives the convex hull of the epigraph in the original QCQP. Our results also imply new sufficient conditions for the tightness (as well as convex hull exactness) of a second order cone program relaxation of simultaneously diagonalizable QCQPs.
In environments where satellite signals are blocked, initializing UAV swarms quickly is a technical challenge, especially indoors or in areas with weak satellite signals, making it difficult to establish the relative ...
详细信息
In environments where satellite signals are blocked, initializing UAV swarms quickly is a technical challenge, especially indoors or in areas with weak satellite signals, making it difficult to establish the relative position of the swarm. Two common methods for initialization are using the camera for joint SLAM initialization, which increases communication burden due to image feature point analysis, and obtaining a rough positional relationship using prior information through a device such as a magnetic compass, which lacks accuracy. In recent years, visual-inertial odometry (VIO) technology has significantly progressed, providing new solutions. With improved computing power and enhanced VIO accuracy, it is now possible to establish the relative position relationship through the movement of drones. This paper proposes a two-stage robust initialization method for swarms of more than four UAVs, suitable for larger-scale satellite denial scenarios. Firstly, the paper analyzes the Cram & eacute;r-Rao lower bound (CRLB) problem and the moving configuration problem of the cluster to determine the optimal anchor node for the algorithm. Subsequently, a strategy is used to screen anchor nodes that are close to the lower bound of CRLB, and an optimization problem is constructed to solve the position relationship between anchor nodes through the relative motion and ranging relationship between UAVs. This optimization problem includes quadratic constraints as well as linear constraints and is a quadratically constrained quadratic programming problem (QCQP) with high robustness and high precision. After addressing the anchor node problem, this paper simplifies and improves a fast swarm cooperative positioning algorithm, which is faster than the traditional multidimensional scaling (MDS) algorithm. The results of theoretical simulations and actual UAV tests demonstrate that the proposed algorithm is advanced, superior, and effectively solves the UAV swarm initialization problem
Explicit model predictive control is an established methodology for the offline determination of the optimal control policy for linear discrete time-invariant systems with linear constraints. Nevertheless, nonlinearit...
详细信息
Explicit model predictive control is an established methodology for the offline determination of the optimal control policy for linear discrete time-invariant systems with linear constraints. Nevertheless, nonlinearities in the form of quadratic constraints naturally appear in process models or are imposed for stability purposes in model predictive control formulations. In this manuscript, we present the theoretical developments and propose an algorithm for the exact solution of explicit nonlinear model predictive control problems with convex quadratic constraints. Our approach is based on a secondorder Taylor approximation of Fiacco's Basic Sensitivity Theorem, which allows for the existence and the analytic derivation of the optimal control actions. The complete exploration of the parameter space is founded on an active set strategy, which employs a pruning criterion to eliminate infeasible active sets. Based on that, the optimal map of solutions is constructed along with the corresponding control actions. The proposed strategy is applied to an explicit nonlinear model predictive control problem with an ellipsoidal terminal set, and comparisons with approximate solutions are drawn to demonstrate the benefits of the presented approach. Furthermore, as a practical application, the optimal operation of a chemostat in the presence of disturbances is exhibited. (C) 2021 Elsevier Ltd. All rights reserved.
We consider the classical convex constrained nonconvex quadraticprogramming problem where the Hessian matrix of the objective to be minimized has r negative eigenvalues, denoted by (QP(r)). Based on a biconvex progra...
详细信息
We consider the classical convex constrained nonconvex quadraticprogramming problem where the Hessian matrix of the objective to be minimized has r negative eigenvalues, denoted by (QP(r)). Based on a biconvex programming reformulation in a slightly higher dimension, we propose a novel branch-and-bound algorithm to solve (QP(1)) and show that it returns an epsilon-approximate solution of (QP(1)) in at most O(1/root epsilon) iterations. We further extend the new algorithm to solve the general (QP(r)) with r > 1. Computational comparison shows the efficiency of our proposed global optimization method for small r. Finally, we extend the explicit relaxation approach for (QP(1)) to (QP(r)) with r > 1.
Mixed-type decision-making is ubiquitously required in robotic systems and has attracted significant research interests. Examples include, but not limited to, the integrated task and motion planning and optimal contro...
详细信息
Mixed-type decision-making is ubiquitously required in robotic systems and has attracted significant research interests. Examples include, but not limited to, the integrated task and motion planning and optimal control of hybrid systems involving both continuous and discrete dynamic behaviors. For decision-making of robotic systems to improve operational efficiency, safety, and/or mission success rate, they involve both discrete variables representing task allocation or transitions between discrete modes and continuous variables representing trajectories of the planned motion or states governed by differential equations. This paper formulates a class of mixed-type decision-making problems with polynomial objective and constraints as quadratically constrained quadratic programming (QCQP) problems and a nonconvex optimization method based on alternating direction method of multipliers is proposed to solve the QCQP. The proposed optimization method consists of three sequential subproblems, all of which admit closed-form solutions. Moreover, convergence proof of the optimization algorithm is provided. Two representative problems, traveling salesman with obstacle avoidance and rendezvous and docking of a charging station with distinct phase constraints, are described and solved via the proposed method. Numerical simulations as well as experimental verification of both problems are presented and compared with a state-of-art method to validate the effectiveness, efficacy and robustness of the nonconvex optimization method.
暂无评论