Convergence properties of a family of inexact Levenberg-Marquardt methods

We present a family of inexact Levenberg-Marquardt (LM) methods for the nonlinear equations which takes more general LM parameters and perturbation vectors. We derive an explicit formula of the convergence order of these inexact LM methods under the H$\mathrm{\ddot{o}}$derian local error bound condition and the H$\mathrm{\ddot{o}}$derian continuity of the Jacobian. Moreover, we develop a family of inexact LM methods with a nonmonotone line search and prove that it is globally convergent. Numerical results for solving the linear complementarity problem are reported

Two-person Graph Convolutional Network for Skeleton-based Human Interaction Recognition

Graph convolutional networks (GCNs) have been the predominant methods in skeleton-based human action recognition, including human-human interaction recognition. However, when dealing with interaction sequences, current GCN-based methods simply split the two-person skeleton into two discrete graphs and perform graph convolution separately as done for single-person action classification. Such operations ignore rich interactive information and hinder effective spatial inter-body relationship modeling. To overcome the above shortcoming, we introduce a novel unified two-person graph to represent inter-body and intra-body correlations between joints. Experiments show accuracy improvements in recognizing both interactions and individual actions when utilizing the proposed two-person graph topology. In addition, We design several graph labeling strategies to supervise the model to learn discriminant spatial-temporal interactive features. Finally, we propose a two-person graph convolutional network (2P-GCN). Our model achieves state-of-the-art results on four benchmarks of three interaction datasets: SBU, interaction subsets of NTU-RGB+D and NTU-RGB+D 120

Compressive hard thresholding pursuit algorithm for sparse signal recovery

Hard Thresholding Pursuit (HTP) is one of the important and efficient algorithms for reconstructing sparse signals. Unfortunately, the hard thresholding operator is independent of the objective function and hence leads to numerical oscillation in the course of iterations. To alleviate this drawback, the hard thresholding operator should be applied to a compressible vector. Motivated by this idea, we propose a new algorithm called Compressive Hard Thresholding Pursuit (CHTP) by introducing a compressive step first to the standard HTP. Convergence analysis and stability of CHTP are established in terms of the restricted isometry property of a sensing matrix. Numerical experiments show that CHTP is competitive with other mainstream algorithms such as the HTP, Orthogonal Matching Pursuit (OMP) and Subspace Pursuit (SP) algorithms both in the sparse signal reconstruction ability and average recovery runtime

IL-21 promotes myocardial ischaemia/reperfusion injury through the modulation of neutrophil infiltration.

BACKGROUND AND PURPOSE: The immune system plays an important role in driving the acute inflammatory response following myocardial ischaemia/reperfusion injury (MIRI). IL-21 is a pleiotropic cytokine with multiple immunomodulatory effects, but its role in MIRI is not known. EXPERIMENTAL APPROACH: Myocardial injury, neutrophil infiltration and the expression of neutrophil chemokines KC (CXCL1) and MIP-2 (CXCL2) were studied in a mouse model of MIRI. Effects of IL-21 on the expression of KC and MIP-2 in neonatal mouse cardiomyocytes (CMs) and cardiac fibroblasts (CFs) were determined by real-time PCR and ELISA. The signalling mechanisms underlying these effects were explored by western blot analysis. KEY RESULTS: IL-21 was elevated within the acute phase of murine MIRI. Neutralization of IL-21 attenuated myocardial injury, as illustrated by reduced infarct size, decreased cardiac troponin T levels and improved cardiac function, whereas exogenous IL-21 administration exerted opposite effects. IL-21 increased the infiltration of neutrophils and increased the expression of KC and MIP-2 in myocardial tissue following MIRI. Moreover, neutrophil depletion attenuated the IL-21-induced myocardial injury. Mechanistically, IL-21 increased the production of KC and MIP-2 in neonatal CMs and CFs, and enhanced neutrophil migration, as revealed by the migration assay. Furthermore, we demonstrated that this IL-21-mediated increase in chemokine expression involved the activation of Akt/NF-κB signalling in CMs and p38 MAPK/NF-κB signalling in CFs. CONCLUSIONS AND IMPLICATIONS: Our data provide novel evidence that IL-21 plays a pathogenic role in MIRI, most likely by promoting cardiac neutrophil infiltration. Therefore, targeting IL-21 may have therapeutic potential as a treatment for MIRI. LINKED ARTICLES: This article is part of a themed section on Spotlight on Small Molecules in Cardiovascular Diseases. To view the other articles in this section visit http://onlinelibrary.wiley.com/doi/10.1111/bph.v175.8/issuetoc

Smoothing functions and algorithm for nonsymmetric circular cone complementarity problems

summary:There has been much interest in studying symmetric cone complementarity problems. In this paper, we study the circular cone complementarity problem (denoted by CCCP) which is a type of nonsymmetric cone complementarity problem. We first construct two smoothing functions for the CCCP and show that they are all coercive and strong semismooth. Then we propose a smoothing algorithm to solve the CCCP. The proposed algorithm generates an infinite sequence such that the value of the merit function converges to zero. Moreover, we show that the iteration sequence must be bounded if the solution set of the CCCP is nonempty and bounded. At last, we prove that the proposed algorithm has local superlinear or quadratical convergence under some assumptions which are much weaker than Jacobian nonsingularity assumption. Some numerical results are reported which demonstrate that our algorithm is very effective for solving CCCPs

New Multiplier Algorithm for Nonlinear Programming with Inequality Constraints

We introduce a new class of augmented Lagrangian function, which includes the well-known essential quadratic augmented Lagrangian as special cases. Based on this new function, we propose a multiplier algorithm, whose main feature is that the multiplier sequence does not require to be bounded. Global convergence to optimal solutions and KKT points are established, respectively

Existence of Generalized Augmented Lagrange Multipliers for Constrained Optimization Problems

The augmented Lagrange multiplier as an important concept in duality theory for optimization problems is extended in this paper to generalized augmented Lagrange multipliers by allowing a nonlinear support for the augmented perturbation function. The existence of generalized augmented Lagrange multipliers is established by perturbation analysis. Meanwhile, the relations among generalized augmented Lagrange multipliers, saddle points, and zero duality gap property are developed

Heavy-Ball-Based Hard Thresholding Pursuit for Sparse Phase Retrieval Problems

We introduce a novel iterative algorithm, termed the Heavy-Ball-Based Hard Thresholding Pursuit for sparse phase retrieval problem (SPR-HBHTP), to reconstruct a sparse signal from a small number of magnitude-only measurements. Our algorithm is obtained via a natural combination of the Hard Thresholding Pursuit for sparse phase retrieval (SPR-HTP) and the classical Heavy-Ball (HB) acceleration method. The robustness and convergence for the proposed algorithm were established with the help of the restricted isometry property. Furthermore, we prove that our algorithm can exactly recover a sparse signal with overwhelming probability in finite steps whenever the initialization is in the neighborhood of the underlying sparse signal, provided that the measurement is accurate. Extensive numerical tests show that SPR-HBHTP has a markedly improved recovery performance and runtime compared to existing alternatives, such as the Hard Thresholding Pursuit for sparse phase retrieval problem (SPR-HTP), the SPARse Truncated Amplitude Flow (SPARTA), and Compressive Phase Retrieval with Alternating Minimization (CoPRAM)

A globally convergent non-interior point algorithm with full Newton step for second-order cone programming

summary:A non-interior point algorithm based on projection for second-order cone programming problems is proposed and analyzed. The main idea of the algorithm is that we cast the complementary equation in the primal-dual optimality conditions as a projection equation. By using this reformulation, we only need to solve a system of linear equations with the same coefficient matrix and compute two simple projections at each iteration, without performing any line search. This algorithm can start from an arbitrary point, and does not require the row vectors of $A$ to be linearly independent. We prove that our algorithm is globally convergent under weak conditions. Preliminary numerical results demonstrate the effectiveness of our algorithm