Related papers: Randomized projection methods for convex feasibili…
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…
We revisit the so-called sampling and discarding approach used to quantify the probability of constraint violation of a solution to convex scenario programs when some of the original samples are allowed to be discarded. Motivated by two…
This paper discusses distributed approaches for the solution of random convex programs (RCP). RCPs are convex optimization problems with a (usually large) number N of randomly extracted constraints; they arise in several applicative areas,…
Solving large-scale systems of nonlinear equations/inequalities is a fundamental problem in computing and optimization. In this paper, we propose a generic successive projection (SP) framework for this problem. The SP sequentially projects…
Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…
Two distributed algorithms are described that enable all users connected over a network to cooperatively solve the problem of minimizing the sum of all users' objective functions over the intersection of all users' constraint sets, where…
A new computationally simple method of imposing hard convex constraints on the neural network output values is proposed. The key idea behind the method is to map a vector of hidden parameters of the network to a point that is guaranteed to…
The randomized version of the Kaczmarz method for the solution of linear systems is known to converge linearly in expectation. In this work we extend this result and show that the recently proposed Randomized Sparse Kaczmarz method for…
An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…
We propose a random coordinate descent algorithm for optimizing a non-convex objective function subject to one linear constraint and simple bounds on the variables. Although it is common use to update only two random coordinates…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…
Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems, various unifying ideas have been introduced, including asymmetric vector-valued norms and…
In this paper, we study randomized and cyclic coordinate descent for convex unconstrained optimization problems. We improve the known convergence rates in some cases by using the numerical semidefinite programming performance estimation…
In this paper, we consider the problem of minimizing the average of a large number of nonsmooth and convex functions. Such problems often arise in typical machine learning problems as empirical risk minimization, but are computationally…
In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate…
The split feasibility problem is to find an element in the intersection of a closed set $C$ and the linear preimage of another closed set $D$, assuming the projections onto $C$ and $D$ are easy to compute. This class of problems arises…
In this paper, a class of convex feasibility problems (CFPs) are studied for multi-agent systems through local interactions. The objective is to search a feasible solution to the convex inequalities with some set constraints in a…
We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…