Related papers: Distance Majorization and Its Applications
In this paper we will discuss two variants of an inexact feasible interior point algorithm for convex quadratic programming. We will consider two different neighbourhoods: a (small) one induced by the use of the Euclidean norm which yields…
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…
The matrix rank minimization problem has applications in many fields such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization…
A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…
A multi-convex optimization problem is one in which the variables can be partitioned into sets over which the problem is convex when the other variables are fixed. Multi-convex problems are generally solved approximately using variations on…
An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate…
Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
In this paper, we modify and apply the recently introduced Mixed Newton Method, which is originally designed for minimizing real-valued functions of complex variables, to the minimization of real-valued functions of real variables by…
An inexact accelerated stochastic Alternating Direction Method of Multipliers (AS-ADMM) scheme is developed for solving structured separable convex optimization problems with linear constraints. The objective function is the sum of a…
A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…
Most existing work uses dual decomposition and subgradient methods to solve Network Utility Maximization (NUM) problems in a distributed manner, which suffer from slow rate of convergence properties. This work develops an alternative…
Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well…
Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…
The constrained minimization (respectively maximization) of directed distances and of related generalized entropies is a fundamental task in information theory as well as in the adjacent fields of statistics, machine learning, artificial…
We investigate the continuous non-monotone DR-submodular maximization problem subject to a down-closed convex solvable constraint. Our first contribution is to construct an example to demonstrate that (first-order) stationary points can…
In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…
One of the most well-known and simplest models for diversity maximization is the Max-Min Diversification (MMD) model, which has been extensively studied in the data mining and database literature. In this paper, we initiate the study of the…
Alternating Direction Method of Multipliers (ADMM) is a popular algorithm for distributed learning, where a network of nodes collaboratively solve a regularized empirical risk minimization by iterative local computation associated with…