Related papers: Random projections for conic programs
Historically, scalability has been a major challenge to the successful application of semidefinite programming in fields such as machine learning, control, and robotics. In this paper, we survey recent approaches for addressing this…
Random Projections have been widely used to generate embeddings for various graph learning tasks due to their computational efficiency. The majority of applications have been justified through the Johnson-Lindenstrauss Lemma. In this paper,…
In this paper, we study the rate of convergence of the cyclic projection algorithm applied to finitely many basic semi-algebraic convex sets. We establish an explicit convergence rate estimate which relies on the maximum degree of the…
In this paper, we extend and investigate the properties of the semi-smooth Newton method when applied to a general projection equation in finite dimensional spaces. We first present results concerning Clarke's generalized Jacobian of the…
Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically,…
We propose a new method for linear second-order cone programs. It is based on the sequential quadratic programming framework for nonlinear programming. In contrast to interior point methods, it can capitalize on the warm-start capabilities…
Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a…
In this paper, we provide an elementary, geometric, and unified framework to analyze conic programs that we call the strict complementarity approach. This framework allows us to establish error bounds and quantify the sensitivity of the…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
The well known constant rank constraint qualification [Math. Program. Study 21:110--126, 1984] introduced by Janin for nonlinear programming has been recently extended to a conic context by exploiting the eigenvector structure of the…
Conic linear programs, among them semidefinite programs, often behave pathologically: the optimal values of the primal and dual programs may differ, and may not be attained. We present a novel analysis of these pathological behaviors. We…
We propose a black-box approach to reducing large semidefinite programs to a set of smaller semidefinite programs by projecting to random linear subspaces. We evaluate our method on a set of polynomial optimization problems, demonstrating…
The projection onto the intersection of sets generally does not allow for a closed form even when the individual projection operators have explicit descriptions. In this work, we systematically analyze the projection onto the intersection…
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
In the last years many results in the area of semidefinite programming were obtained for invariant (finite dimensional, or infinite dimensional) semidefinite programs - SDPs which have symmetry. This was done for a variety of problems and…
Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In…
The completely bounded trace and spectral norms, for finite-dimensional spaces, are known to be efficiently expressible by semidefinite programs (J. Watrous, Theory of Computing 5: 11, 2009). This paper presents two new, and arguably much…
We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…