We investigate the multi-dimensional Super Resolution problem on closed semi-algebraic domains for various sampling schemes such as Fourier or moments. We present a new semidefinite programming (SDP) formulation of the l1-minimization in the space of Radon measures in the multi-dimensional frame on semi-algebraic sets. While standard approaches have focused on SDP relaxations of the dual … Read more
In this paper, we propose a new step size rule to accelerate Yan et al.’s self-adaptive projection method. Under the new step size strategy, the superiority of modified projection method is verified through theory to numerical experiments. CitationCollege of Communications Engineering, PLA University of Science and Technology, Nanjing, 210007, China 01/29/2015ArticleDownload View PDF
In this work we consider the feature ranking problem where, given a set of training instances, the task is to associate a score to the features in order to assess their relevance. Feature ranking is a very important tool for decision support systems, and may be used as an auxiliary step of feature selection to … Read more
In this paper we propose a new way to compute a warm starting point for a challenging global optimization problem related to Earth imaging in geophysics. The warm start consists of a velocity model that approximately solves a full-waveform inverse problem at low frequency. Our motivation arises from the availability of massively parallel computing platforms … Read more
We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing system has access to a local empirical loss function, constructed with i.i.d. data sampled from a common distribution. We propose a communication-efficient distributed algorithm to … Read more
The minimization of volume constrained vector-valued Ginzburg-Landau energy functional is considered in the present study. It has many applications in computational science and engineering, like the conservative phase separation in multiphase systems (such as the spinodal decomposition), phase coarsening in multiphase systems, color image segmentation and optimal space partitioning. A computationally efficient algorithm is presented … Read more
The objective of dynamic economic dispatch (DED) problem is to find the optimal dispatch of generation units in a given operation horizon to supply a pre-specified demand, while satisfying a set of constraints. In this paper, an efficient method based on Optimality Condition Decomposition (OCD) technique is proposed to solve the DED problem in real-time … Read more
Vulnerability of power grid is a critical issue in power industry. In order to understand and reduce power grid vulnerability under threats, existing research often employs defender-attacker-defender (DAD) models to derive effective protection plans and evaluate grid performances under various contingencies. Transmission line switching (also known as topology control) is an effective operation to mitigate … Read more
It is well-known that optimizing network topology by switching on and off transmission lines improves the efficiency of power delivery in electrical networks. In fact, the USA Energy Policy Act of 2005 (Section 1223) states that the U.S. should “encourage, as appropriate, the deployment of advanced transmission technologies” including “optimized transmission line configurations”. As such, … Read more
The study of matrix inequalities in a dimension-free setting is in the realm of free real algebraic geometry (RAG). In this paper we investigate constrained trace and eigenvalue optimization of noncommutative polynomials. We present Lasserre’s relaxation scheme for trace optimization based on semidefinite programming (SDP) and demonstrate its convergence properties. Finite convergence of this relaxation … Read more