Minimum-monitor-unit optimization via a stochastic coordinate descent method

Objective: Deliverable proton spots are subject to the minimum monitor-unit (MMU) constraint. The MMU optimization problem with relatively large MMU threshold remains mathematically challenging due to its strong nonconvexity. However, the MMU optimization is fundamental to proton radiotherapy (RT), including efficient IMPT, proton arc delivery (ARC), and FLASH-RT. This work aims to develop a new optimization algorithm that is effective in solving the MMU problem. Approach: Our new algorithm is primarily based on stochastic coordinate decent (SCD) method. It involves three major steps: first to decouple the determination of active sets for dose-volume-histogram (DVH) planning constraints from the MMU problem via iterative convex relaxation method; second to handle the nonconvexity of the MMU constraint via SCD to localize the index set of nonzero spots; third to solve convex subproblems projected to this convex set of nonzero spots via projected gradient descent method. Main results: Our new method SCD is validated and compared with alternating direction method of multipliers (ADMM) for IMPT and ARC. The results suggest SCD had better plan quality than ADMM, e.g., the improvement of conformal index (CI) from 0.51 to 0.71 during IMPT, and from 0.22 to 0.86 during ARC for the lung case. Moreover, SCD successfully handled the nonconvexity from large MMU threshold that ADMM failed to handle, in the sense that (1) the plan quality from ARC was worse than IMPT (e.g., CI was 0.51 with IMPT and 0.22 with ARC for the lung case), when ADMM was used; (2) in contrast, with SCD, ARC achieved better plan quality than IMPT (e.g., CI was 0.71 with IMPT and 0.86 with ARC for the lung case), which is compatible with more optimization degrees of freedom from ARC compared to IMPT. Significance: To the best of our knowledge, our new MMU optimization method via SCD can effectively handle the nonconvexity from large MMU threshold that none of the current methods can solve. Therefore, we have developed a unique MMU optimization algorithm via SCD that can be used for efficient IMPT, proton arc delivery (ARC), FLASH-RT, and other particle RT applications where large MMU threshold is desirable (e.g., for the delivery of high dose rates or/and a large number of spots).

Block-Sparse Recovery with Optimal Block Partition

This paper presents a convex recovery method for block-sparse signals whose block partitions are unknown a priori. We first introduce a nonconvex penalty function, where the block partition is adapted for the signal of interest by minimizing the mixed l2/l1 norm over all possible block partitions. Then, by exploiting a variational representation of the l2 norm, we derive the proposed penalty function as a suitable convex relaxation of the nonconvex one. For a block-sparse recovery model designed with the proposed penalty, we develop an iterative algorithm which is guaranteed to converge to a globally optimal solution. Numerical experiments demonstrate the effectiveness of the proposed method.

An Improved PMU Data Manipulation Attack Model

The importance of Phasor Manipulation Unit (PMU) in the smart grid makes it a target for attackers who can create PMU Data Manipulation Attacks (PDMA) by adding a small constant to change the magnitude and angle of the voltage and current captured by the PMU. To prevent the attack result from being detected by PDMA detection based on the properties of equivalent impedance, this paper proposes a collaborative step attack. In this attack, the equivalent impedance’s value on the end of the transmission line is equal whether before or after been attack, which is taken as the constraint condition. The objective function of it is to minimize the number of the elements which is not 0 in attack vector but this number is not 0. Turn a vector construction problem into an optimization problem by building objective functions and constraints and then we use the Alternating Direction Method of Multipliers (ADMM) and Convex Relaxation (CR) to solve. The experiment verifies the feasibility of using the CR-ADMM algorithm to construct attack vectors from two aspects of attack vector construction time and vector sparsity. Further, it uses the constructed attack vectors to carry out attacks on PMU. The experimental results show that the measurement value of PMU will change after the attack, but the equivalent impedance value at both ends of the transmission line remains the same. The attack vector successfully bypasses the PDMA detection method based on the property of equivalent impedance and the attack model constructed based on this method was more covert than the original model.

The Non-Tightness of a Convex Relaxation to Rotation Recovery

We study the Perspective-n-Point (PNP) problem, which is fundamental in 3D vision, for the recovery of camera translation and rotation. A common solution applies polynomial sum-of-squares (SOS) relaxation techniques via semidefinite programming. Our main result is that the polynomials which should be optimized can be non-negative but not SOS, hence the resulting convex relaxation is not tight; specifically, we present an example of real-life configurations for which the convex relaxation in the Lasserre Hierarchy fails, in both the second and third levels. In addition to the theoretical contribution, the conclusion for practitioners is that this commonly-used approach can fail; our experiments suggest that using higher levels of the Lasserre Hierarchy reduces the probability of failure. The methods we use are mostly drawn from the area of polynomial optimization and convex relaxation; we also use some results from real algebraic geometry, as well as Matlab optimization packages for PNP.

A column generation algorithm for solving energy system planning problems

Energy system optimization models are typically large models which combine sub-models which range from linear to very nonlinear. Column generation (CG) is a classical tool to generate feasible solutions of sub-models, defining columns of global master problems, which are used to steer the search for a global solution. In this paper, we present a new inner approximation method for solving energy system MINLP models. The approach is based on combining CG and the Frank Wolfe algorithm for generating an inner approximation of a convex relaxation and a primal heuristic for computing solution candidates. The features of this approach are: (i) no global branch-and-bound tree is used, (ii) sub-problems can be solved in parallel to generate columns, which do not have to be optimal, nor become available at the same time to synchronize the solution, (iii) an arbitrary solver can be used to solve sub-models, (iv) the approach (and the implementation) is generic and can be used to solve other nonconvex MINLP models. We perform experiments with decentralized energy supply system models with more than 3000 variables. The numerical results show that the new decomposition method is able to compute high-quality solutions and has the potential to outperform state-of-the-art MINLP solvers.

A Highly Scalable Method for Extractive Text Summarization Using Convex Optimization

The paper describes a convex optimization formulation of the extractive text summarization problem and a simple and scalable algorithm to solve it. The optimization program is constructed as a convex relaxation of an intuitive but computationally hard integer programming problem. The objective function is highly symmetric, being invariant under unitary transformations of the text representations. Another key idea is to replace the constraint on the number of sentences in the summary with a convex surrogate. For solving the program we have designed a specific projected gradient descent algorithm and analyzed its performance in terms of execution time and quality of the approximation. Using the datasets DUC 2005 and Cornell Newsroom Summarization Dataset, we have shown empirically that the algorithm can provide competitive results for single document summarization and multi-document query-based summarization. On the Cornell Newsroom Summarization Dataset, it ranked second among the unsupervised methods tested. For the more challenging task of multi-document query-based summarization, the method was tested on the DUC 2005 Dataset. Our algorithm surpassed the other reported methods with respect to the ROUGE-SU4 metric, and it was at less than 0.01 from the top performing algorithms with respect to ROUGE-1 and ROUGE-2 metrics.

Hyperspectral Image Denoising via Framelet Transformation Based Three-Modal Tensor Nuclear Norm

During the acquisition process, hyperspectral images (HSIs) are inevitably contaminated by mixed noise, which seriously affects the image quality. To improve the image quality, HSI denoising is a critical preprocessing step. In HSI denoising tasks, the method based on low-rank prior has achieved satisfying results. Among numerous denoising methods, the tensor nuclear norm (TNN), based on the tensor singular value decomposition (t-SVD), is employed to describe the low-rank prior approximately. Its calculation can be sped up by the fast Fourier transform (FFT). However, TNN is computed by the Fourier transform, which lacks the function of locating frequency. Besides, it only describes the low-rankness of the spectral correlations and ignores the spatial dimensions’ information. In this paper, to overcome the above deficiencies, we use the basis redundancy of the framelet and the low-rank characteristics of HSI in three modes. We propose the framelet-based tensor fibered rank as a new representation of the tensor rank, and the framelet-based three-modal tensor nuclear norm (F-3MTNN) as its convex relaxation. Meanwhile, the F-3MTNN is the new regularization of the denoising model. It can explore the low-rank characteristics of HSI along three modes that are more flexible and comprehensive. Moreover, we design an efficient algorithm via the alternating direction method of multipliers (ADMM). Finally, the numerical results of several experiments have shown the superior denoising performance of the proposed F-3MTNN model.