Related papers: The Pivoting Framework: Frank-Wolfe Algorithms wit…
In this paper, we use composite optimization algorithms to solve sigmoid networks. We equivalently transfer the sigmoid networks to a convex composite optimization and propose the composite optimization algorithms based on the linearized…
In many online learning problems the computational bottleneck for gradient-based methods is the projection operation. For this reason, in many problems the most efficient algorithms are based on the Frank-Wolfe method, which replaces…
The stochastic Frank-Wolfe method has recently attracted much general interest in the context of optimization for statistical and machine learning due to its ability to work with a more general feasible region. However, there has been a…
The paper presents various modifications of the Frank-Wolfe algorithm in the equilibrium traffic assignment problem. The Beckman model is used as a model for experiments. In this article, first of all, attention is paid to the choice of the…
We propose a new iteration scheme, the Cauchy-Simplex, to optimize convex problems over the probability simplex $\{w\in\mathbb{R}^n\ |\ \sum_i w_i=1\ \textrm{and}\ w_i\geq0\}$. Specifically, we map the simplex to the positive quadrant of a…
Projection operations are a typical computation bottleneck in online learning. In this paper, we enable projection-free online learning within the framework of Online Convex Optimization with Memory (OCO-M) -- OCO-M captures how the history…
Dense conditional random fields (CRF) with Gaussian pairwise potentials have emerged as a popular framework for several computer vision applications such as stereo correspondence and semantic segmentation. By modeling long-range…
In this paper we present an active-set method for the solution of $\ell_1$-regularized convex quadratic optimization problems. It is derived by combining a proximal method of multipliers (PMM) strategy with a standard semismooth Newton…
In this note we observe that for constrained convex minimization problems $\min_{x \in P}f(x)$ over a polytope $P$, dual prices for the linear program $\min_{z \in P} \nabla f(x) z$ obtained from linearization at approximately optimal…
We analyze two novel randomized variants of the Frank-Wolfe (FW) or conditional gradient algorithm. While classical FW algorithms require solving a linear minimization problem over the domain at each iteration, the proposed method only…
Projection-free optimization via different variants of the Frank-Wolfe (FW), a.k.a. Conditional Gradient method has become one of the cornerstones in optimization for machine learning since in many cases the linear minimization oracle is…
In this paper, we focus on solving a distributed convex aggregative optimization problem in a network, where each agent has its own cost function which depends not only on its own decision variables but also on the aggregated function of…
The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space…
Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…
Infinite-horizon optimal control of constrained piecewise affine (PWA) systems has been approximately addressed by hybrid model predictive control (MPC), which, however, has computational limitations, both in offline design and online…
The optimal transport (OT) problem has been used widely for machine learning. It is necessary for computation of an OT problem to solve linear programming with tight mass-conservation constraints. These constraints prevent its application…
We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP…
Frank-Wolfe (FW) algorithms have emerged as an essential class of methods for constrained optimization, especially on large-scale problems. In this paper, we summarize the algorithmic design choices and progress made in the last years of…
In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe…
We propose a feasible active set method for convex quadratic programming problems with non-negativity constraints. This method is specifically designed to be embedded into a branch-and-bound algorithm for convex quadratic mixed integer…