Related papers: An augmented Lagrangian model for signal segmentat…
This paper proposes a novel approach to solving nonlinear programming problems using a sharp augmented Lagrangian method with a smoothing technique. Traditional sharp augmented Lagrangian methods are known for their effectiveness but are…
The twin support vector machine and its extensions have made great achievements in dealing with binary classification problems. However, it suffers from difficulties in effective solution of multi-classification and fast model selection.…
This study presents a rapid multiple incremental and decremental mechanism based on Weight-Error Curves (WECs) for support-vector analysis. Recursion-free computation is proposed for predicting the Lagrangian multipliers of new samples.…
We propose enhancements to score-based generative modeling techniques for low-latency pilot-based channel estimation in a point-to-point single-carrier multiple-input multiple-output (MIMO) wireless system. Building on recent advances in…
In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the…
This paper analyzes the contraction of the primal-dual gradient optimization via contraction theory in the context of discrete-time updating dynamics. The contraction theory based on Riemannian manifolds is first established for convergence…
In this work, we investigate the large-scale mean-field variational inference (MFVI) problem from a mini-batch primal-dual perspective. By reformulating MFVI as a constrained finite-sum problem, we develop a novel primal-dual algorithm…
A bilevel training scheme is used to introduce a novel class of regularizers, providing a unified approach to standard regularizers $TV$, $TGV^2$ and $NsTGV^2$. Optimal parameters and regularizers are identified, and the existence of a…
Euler's elastica model has been extensively studied and applied to image processing tasks. However, due to the high nonlinearity and nonconvexity of the involved curvature term, conventional algorithms suffer from slow convergence and high…
Second-order sufficient conditions for local optimality have been playing an important role in local convergence analysis of optimization algorithms. In this paper, we demonstrate that this condition alone suffices to justify the linear…
In this paper we show that any increasing functional of the first k eigenvalues of the Dirichlet Laplacian admits a (quasi-)open minimizer among the subsets of R^N of unit measure. In particular, there exists such a minimizer which is…
Joint peak detection is a central problem when comparing samples in genomic data analysis, but current algorithms for this task are unsupervised and limited to at most 2 sample types. We propose PeakSegJoint, a new constrained maximum…
Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical integrators. The phase space of such variational…
We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…
The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact…
This paper introduces a coordinate descent version of the V\~u-Condat algorithm. By coordinate descent, we mean that only a subset of the coordinates of the primal and dual iterates is updated at each iteration, the other coordinates being…
The Chan-Vese (CV) model is a classic region-based method in image segmentation. However, its piecewise constant assumption does not always hold for practical applications. Many improvements have been proposed but the issue is still far…
We study the minmax optimization problem introduced in [22] for computing policies for batch mode reinforcement learning in a deterministic setting. First, we show that this problem is NP-hard. In the two-stage case, we provide two…
With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness…
Convex optimization models find interesting applications, especially in signal/image processing and compressive sensing. We study some augmented convex models, which are perturbed by strongly convex functions, and propose a dual gradient…