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The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…
In this paper, an efficient modified Newton type algorithm is proposed for nonlinear unconstrianed optimization problems. The modified Hessian is a convex combination of the identity matrix (for steepest descent algorithm) and the Hessian…
We present a generic coordinate descent solver for the minimization of a nonsmooth convex objective with structure. The method can deal in particular with problems with linear constraints. The implementation makes use of efficient residual…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
In this paper we analyze boosting algorithms in linear regression from a new perspective: that of modern first-order methods in convex optimization. We show that classic boosting algorithms in linear regression, namely the incremental…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
In this paper, we study a class of problems where the sum of truncated convex functions is minimized. In statistical applications, they are commonly encountered when $\ell_0$-penalized models are fitted and usually lead to NP-Hard…
In this paper, we introduce a stochastic projected subgradient method for weakly convex (i.e., uniformly prox-regular) nonsmooth, nonconvex functions---a wide class of functions which includes the additive and convex composite classes. At a…
In this paper, we utilize stochastic optimization to reduce the space complexity of convex composite optimization with a nuclear norm regularizer, where the variable is a matrix of size $m \times n$. By constructing a low-rank estimate of…
In this paper we propose a subgradient algorithm for solving the equilibrium problem where the bifunction may be quasiconvex with respect to the second variable. The convergence of the algorithm is investigated. A numerical example for a…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of…
In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal…
In this paper, we introduce an unbiased gradient simulation algorithms for solving convex optimization problem with stochastic function compositions. We show that the unbiased gradient generated from the algorithm has finite variance and…
A specialized algorithm for quadratic optimization (QO, or, formerly, QP) with disjoint linear constraints is presented. In the considered class of problems, a subset of variables are subject to linear equality constraints, while variables…
Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…
Solving structured systems of linear equations in a non-centralized fashion is an important step in many distributed optimization and control algorithms. Fast convergence is required in manifold applications. Known decentralized algorithms,…
We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where…
We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related…