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Showing 1 to 17 of 17 for “"semidefinite programming (SDP)"”.
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Low rank decompositions for sum of squares optimization
… barrier gradient and Hessian assembling in many semidefinite programming (SDP) solvers. Currently, SDPT3 solver has a function to store low rank constraints to explore its numerical advantages. Some SOS examples are constructed and tested on SDPT3 to a great extent. The experimental results …
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Semidefinite relaxation based branch-and-bound method for nonconvex quadratic programming
In this thesis, we use a semidefinite relaxation based branch-and-bound method to solve nonconvex quadratic programming problems. Firstly, we show an interval branch-and-bound method to calculate the bounds for the minimum of bounded polynomials. Then we demonstrate four SDP relaxation methods to …
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Inference of 3D structure of diploid chromosomes
… into noisy distance measurements and then apply semidefinite programming (SDP) formulations to obtain the 3D configurations. However, neglected in such reconstructions is the fact that most eukaryotes including humans are diploid and therefore contain two (from the available data) …
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Control of quad-rotor UAVs using switched-system synthesis methods
… The methodologies of LQR control and semidefinite programming (SDP) are discussed to provide preliminary knowledge of the switched control. Benefits of the LQR control include tracking of reference trajectories and cost function minimization. The core of switched control methods is the …
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Discrete-continuous optimization for robot perception via semidefinite relaxation
… we propose polynomial-time algorithms based on semidefinite programming (SDP) relaxation to find approximate solutions to nonconvex problems arising in two fields of robot perception, semantic segmentation and robust pose graph optimization. Compared with other inference techniques, SDP …
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Certifiable Outlier-Robust Geometric Perception
… and (ii) a certifier that employs sparse semidefinite programming (SDP) relaxation and a novel SDP solver to endow the estimator with an optimality certificate or escape local minima otherwise. The estimator is fast and robust against up to 60% − 99% random outliers in practical perception …
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Power and limitations of convex formulations via linear and semidefinite programming lifts
… and develop lower bounds on the sizes of linear programming (LP) and semidefinite programming (SDP) lifts of polytopes. For LP lifts the bound we develop applies generally for the nonnegative rank of matrices and we compare our method with existing combinatorial and non-combinatorial techniques. …
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Cooperative Positioning in Wireless Sensor Networks Using Semidefinite Programming
… as a recent and trending technology and semidefinite programming (SDP) as a powerful tool in our research. Cooperative localization has several advantages over the traditional noncooperative localization in terms of positioning accuracy and localizability. Cooperation is also highly …
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Polynomial Optimization and the Moment Problem
… most successful approaches to this problem is semidefinite programming (SDP), which gives a polynomial time method to approximate the largest real number $r$ such that f-r is a sum of squares of polynomials. But current implementations of SDP are not able to minimize polynomials in rather small …
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Model-based robust and stochastic control, and statistical inference for uncertain dynamical systems
… control methods are proposed in terms of conic programming that includes linear programming and semidefinite programming (SDP). For stochastic uncertain models and stochastic control, uncertainties are described in terms of probability distribution functions. Stability and performance …
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Algorithmic advances in range-aided navigation
… for these solutions. CORA leverages a novel semidefinite programming (SDP) relaxation of the RA-SLAM problem, which it solves efficiently using the Riemannian Staircase methodology. This methodology allows CORA to typically obtain globally optimal solutions faster than the existing …
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Algorithmic Advances in Range-Aided Navigation
… for these solutions. CORA leverages a novel semidefinite programming (SDP) relaxation of the RA-SLAM problem, which it solves efficiently using the Riemannian Staircase methodology. This methodology allows CORA to typically obtain globally optimal solutions faster than the existing …
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Subset sum and community problems: From social to geometry
… initial ``hidden'' partition of $[n]$. We study semidefinite programming (SDP) based algorithms in this context. In the regime $p = \frac{\alpha \log(m)}{m}$ and $q = \frac{\beta \log(m)}{m}$ we show that a certain natural SDP based algorithm solves the problem of {\em exact recovery} in the …
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Polynomial systems : graphical structure, geometry, and applications
… Although these problems are nonconvex, tractable semidefinite programming (SDP) relaxations have been proposed. We introduce a methodology to derive more efficient (smaller) relaxations, by leveraging the geometrical structure of the underlying variety. The main idea behind our method is to …
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Renewable Energy Integration in Distribution System with Artificial Intelligence
… with OPF in real-time (RT) scheduling. The semidefinite programming (SDP) is used to relax the nonconvexity of the three-phase unbalanced distribution system into a convex problem, which helps to achieve the global optimal result. In the parallel manner, the ADMM is realizing getting the …
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Resource allocation and secure communication design in simultaneous wireless information and power transfer systems
… The non-convex problem is converted into a semidefinite programming (SDP) problem by using the semidefinite relaxation (SDR) approach. In addition, a rank-one proof presents that the solution generated by the relaxed problem is optimal to the original problem. Second, a security issue about …
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Semidefinite Cuts and Partial Convexification Techniques with Applications to Continuous Nonconvex Optimization, Stochastic Integer Programming, and Facility Layout Problems
… the use of a new class of RLT cuts, called semidefinite cuts. While these cuts are valid for any general problem for which RLT is applicable, we demonstrate their effectiveness in optimizing a nonconvex quadratic objective function over a simplex. Computational results indicate that on …