Related papers: Differentiating the Value Function by using Convex…
The paper is about developing a solver for maximizing a real-valued function of binary variables. The solver relies on an algorithm that estimates the optimal objective-function value of instances from the underlying distribution of…
We analyze matrix convex functions of a fixed order defined on a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus. We obtain for each order conditions for matrix…
In this paper we propose distributed dual gradient algorithms for linearly constrained separable convex problems and analyze their rate of convergence under different assumptions. Under the strong convexity assumption on the primal…
We consider smooth stochastic convex optimization problems in the context of algorithms which are based on directional derivatives of the objective function. This context can be considered as an intermediate one between derivative-free…
Deep learning has been applied to various tasks in the field of machine learning and has shown superiority to other common procedures such as kernel methods. To provide a better theoretical understanding of the reasons for its success, we…
Vertex direction algorithms have been around for a few decades in the experimental design and mixture models literature. We briefly review this type of algorithm and describe a new member of the family: the support reduction algorithm. The…
Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization…
We derive approximation algorithms for the nonnegative matrix factorization problem, i.e. the problem of factorizing a matrix as the product of two matrices with nonnegative coefficients. We form convex approximations of this problem which…
Submodularity is one of the most well-studied properties of problem classes in combinatorial optimization and many applications of machine learning and data mining, with strong implications for guaranteed optimization. In this thesis, we…
We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum $\sum_{i=1}^{m}f_i(z)$ of functions over in a network. We provide complexity bounds for four different…
We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems, and thus are well suitable for primal-dual first-order algorithms. However,…
The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying…
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…
A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a…
This paper investigates a specific class of nonsmooth nonconvex optimization problems in the face of data uncertainty, namely, robust optimization problems, where the given objective function can be expressed as a difference of two…
In optimization the duality gap between the primal and the dual problems is a measure of the suboptimality of any primal-dual point. In classical mechanics the equations of motion of a system can be derived from the Hamiltonian function,…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
Originally designed for applications in computer graphics, visual computing (VC) methods synthesize information about physical and virtual worlds, using prescribed algorithms optimized for spatial computing. VC is used to analyze geometry,…
Despite the recent development in machine learning, most learning systems are still under the concept of "black box", where the performance cannot be understood and derived. With the rise of safety and privacy concerns in public, designing…
This works aims at understanding further convergence properties of first order local search methods with complex geometries. We focus on the composite optimization model which unifies within a simple formalism many problems of this type. We…