The box-constrained weighted maximin dispersion problem is to find a point in an n-dimensional box such that the minimum of the weighted Euclidean distance from given m points is maximized. In this paper, we first ref...The box-constrained weighted maximin dispersion problem is to find a point in an n-dimensional box such that the minimum of the weighted Euclidean distance from given m points is maximized. In this paper, we first reformulate the maximin dispersion problem as a non-convex quadratically constrained quadratic programming (QCQP) problem. We adopt the successive convex approximation (SCA) algorithm to solve the problem. Numerical results show that the proposed algorithm is efficient.展开更多
We establish in this paper optimal parametric Lagrangian dual models for box constrained quadratic program based on the generalized D.C.(difference between convex) optimization approach,which can be reformulated as se...We establish in this paper optimal parametric Lagrangian dual models for box constrained quadratic program based on the generalized D.C.(difference between convex) optimization approach,which can be reformulated as semidefinite programming problems.As an application,we propose new valid linear constraints for rank-one relaxation.展开更多
Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by exp...Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods,it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.展开更多
非视距(non-line-of-sight,NLOS)误差是导致室内定位精度低、稳定性差的一个重要原因,现有NLOS误差抑制算法存在复杂度较高、鲁棒性较差等问题。提出一种基于凸优化方法的室内NLOS误差抑制算法,为保证定位鲁棒性,该算法先给出鲁棒最小二...非视距(non-line-of-sight,NLOS)误差是导致室内定位精度低、稳定性差的一个重要原因,现有NLOS误差抑制算法存在复杂度较高、鲁棒性较差等问题。提出一种基于凸优化方法的室内NLOS误差抑制算法,为保证定位鲁棒性,该算法先给出鲁棒最小二乘(robust least squares,RLS)形式的位置估计问题,再依据遮挡情况不同,将定位环境分为轻微遮挡环境和严重遮挡环境,并根据两种环境NLOS误差特性,引入新的松弛条件,将上述位置估计问题分别转化为二次约束二次规划问题和二阶锥规划问题并求解。仿真实验表明,相比已有算法,在不同应用场景下,所提算法提高了定位精度,并且有效降低了无解个数,增强了鲁棒性。展开更多
文摘The box-constrained weighted maximin dispersion problem is to find a point in an n-dimensional box such that the minimum of the weighted Euclidean distance from given m points is maximized. In this paper, we first reformulate the maximin dispersion problem as a non-convex quadratically constrained quadratic programming (QCQP) problem. We adopt the successive convex approximation (SCA) algorithm to solve the problem. Numerical results show that the proposed algorithm is efficient.
基金supported by National Natural Science Foundation of China(Grant Nos. 11001006 and 91130019/A011702)the Fund of State Key Laboratory of Software Development Environment (Grant No. SKLSDE-2011ZX-15.)
文摘We establish in this paper optimal parametric Lagrangian dual models for box constrained quadratic program based on the generalized D.C.(difference between convex) optimization approach,which can be reformulated as semidefinite programming problems.As an application,we propose new valid linear constraints for rank-one relaxation.
基金supported by the National Natural Science Foundation of China(Grant Nos.10171104,10571171&40233029).
文摘Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods,it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.
文摘非视距(non-line-of-sight,NLOS)误差是导致室内定位精度低、稳定性差的一个重要原因,现有NLOS误差抑制算法存在复杂度较高、鲁棒性较差等问题。提出一种基于凸优化方法的室内NLOS误差抑制算法,为保证定位鲁棒性,该算法先给出鲁棒最小二乘(robust least squares,RLS)形式的位置估计问题,再依据遮挡情况不同,将定位环境分为轻微遮挡环境和严重遮挡环境,并根据两种环境NLOS误差特性,引入新的松弛条件,将上述位置估计问题分别转化为二次约束二次规划问题和二阶锥规划问题并求解。仿真实验表明,相比已有算法,在不同应用场景下,所提算法提高了定位精度,并且有效降低了无解个数,增强了鲁棒性。
