On the Optimal Linear Convergence Rate of a Generalized Proximal Point Algorithm

The proximal point algorithm (PPA) has been well studied in the literature. In particular, its linear convergence rate has been studied by Rockafellar in 1976 under certain condition. We consider a generalized PPA in the generic setting of finding a zero point of a maximal monotone operator, and show that the condition proposed by Rockafellar can also sufficiently ensure the linear convergence rate for this generalized PPA. Indeed we show that these linear convergence rates are optimal. Both the exact and inexact versions of this generalized PPA are discussed. The motivation to consider this generalized PPA is that it includes as special cases the relaxed versions of some splitting methods that are originated from PPA. Thus, linear convergence results of this generalized PPA can be used to better understand the convergence of some widely used algorithms in the literature. We focus on the particular convex minimization context and specify Rockafellar's condition to see how to ensure the linear convergence rate for some efficient numerical schemes, including the classical augmented Lagrangian method proposed by Hensen and Powell in 1969 and its relaxed version, the original alternating direction method of multipliers (ADMM) by Glowinski and Marrocco in 1975 and its relaxed version (i.e., the generalized ADMM by Eckstein and Bertsekas in 1992). Some refined conditions weaker than existing ones are proposed in these particular contexts.Comment: 22 pages, 1 figur

Anti-dark and Mexican-hat solitons in the Sasa-Satsuma equation on the continuous wave background

In this letter, via the Darboux transformation method we construct new analytic soliton solutions for the Sasa-Satsuma equation which describes the femtosecond pulses propagation in a monomode fiber. We reveal that two different types of femtosecond solitons, i.e., the anti-dark (AD) and Mexican-hat (MH) solitons, can form on a continuous wave (CW) background, and numerically study their stability under small initial perturbations. Different from the common bright and dark solitons, the AD and MH solitons can exhibit both the resonant and elastic interactions, as well as various partially/completely inelastic interactions which are composed of such two fundamental interactions. In addition, we find that the energy exchange between some interacting soliton and the CW background may lead to one AD soliton changing into an MH one, or one MH soliton into an AD one.Comment: 12 pages, 6 figure

Efficient Online Quantum Generative Adversarial Learning Algorithms with Applications

The exploration of quantum algorithms that possess quantum advantages is a central topic in quantum computation and quantum information processing. One potential candidate in this area is quantum generative adversarial learning (QuGAL), which conceptually has exponential advantages over classical adversarial networks. However, the corresponding learning algorithm remains obscured. In this paper, we propose the first quantum generative adversarial learning algorithm-- the quantum multiplicative matrix weight algorithm (QMMW)-- which enables the efficient processing of fundamental tasks. The computational complexity of QMMW is polynomially proportional to the number of training rounds and logarithmically proportional to the input size. The core concept of the proposed algorithm combines QuGAL with online learning. We exploit the implementation of QuGAL with parameterized quantum circuits, and numerical experiments for the task of entanglement test for pure state are provided to support our claims

Pseudo-goldstino and electroweakinos via VBF processes at LHC

The multi-sector SUSY breaking predicts pseudo-goldstino which can couple to the visible sector more strongly than the ordinary gavitino and thus induce the decays of the lightest neutralino and chargino (collectively called electroweakinos) inside the detector. In this note we study the electroweakino pair productions via vector boson fusion (VBF) processes followed by decays to pseudo-goldstino at the LHC. Our Monte Carlo simulations show that at the 14 TeV LHC with 3000 fb^{-1} luminosity the dominant production channel pp->chargino+neutralino+2 jets can have a statistical significance above 2-sigma while other production channels are not accessible.Comment: Version in JHEP (comments added

MiniMax Entropy Network: Learning Category-Invariant Features for Domain Adaptation

How to effectively learn from unlabeled data from the target domain is crucial for domain adaptation, as it helps reduce the large performance gap due to domain shift or distribution change. In this paper, we propose an easy-to-implement method dubbed MiniMax Entropy Networks (MMEN) based on adversarial learning. Unlike most existing approaches which employ a generator to deal with domain difference, MMEN focuses on learning the categorical information from unlabeled target samples with the help of labeled source samples. Specifically, we set an unfair multi-class classifier named categorical discriminator, which classifies source samples accurately but be confused about the categories of target samples. The generator learns a common subspace that aligns the unlabeled samples based on the target pseudo-labels. For MMEN, we also provide theoretical explanations to show that the learning of feature alignment reduces domain mismatch at the category level. Experimental results on various benchmark datasets demonstrate the effectiveness of our method over existing state-of-the-art baselines.Comment: 8 pages, 6 figure