Related papers: Random projections for conic programs
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
We use principal angles between two subspaces to define Jordan planes. Jordan planes provide an optimal way to decompose $\mathbb{C}^n$ in relation to given two subspaces. We apply Jordan planes to show that two pairs of of subspaces…
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
This is a tutorial and survey paper on the Johnson-Lindenstrauss (JL) lemma and linear and nonlinear random projections. We start with linear random projection and then justify its correctness by JL lemma and its proof. Then, sparse random…
In this paper, we study classes of structures and individual structures for which programs implementing functions defined everywhere are equivalent to finite tree-programs. The programs under consideration may have cycles and at most…
This paper is devoted to the investigation of selected situations when the computation of projective (and other) equivalences of algebraic varieties can be efficiently solved with the help of finding projective equivalences of finite sets…
We observe that the characteristic polynomial of a linearly perturbed semidefinite matrix can be used to give the convergence rate of alternating projections for the positive semidefinite cone and a line. As a consequence, we show that such…
In this paper, we introduce methods of encoding propositional logic programs in vector spaces. Interpretations are represented by vectors and programs are represented by matrices. The least model of a definite program is computed by…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
The goal of this paper is to investigate new and simple convergence analysis of dynamic programming for linear quadratic regulator problem of discrete-time linear time-invariant systems. In particular, bounds on errors are given in terms of…
The subject of this work is quantum predicative programming -- the study of developing of programs intended for execution on a quantum computer. We look at programming in the context of formal methods of program development, or programming…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…
In a previous paper [R. Andreani, G. Haeser, L. M. Mito, H. Ram\'irez, T. P. Silveira. First- and second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition. Mathematical…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
We present an algorithm for approximating semidefinite programs with running time that is sublinear in the number of entries in the semidefinite instance. We also present lower bounds that show our algorithm to have a nearly optimal running…
We consider the problem of constructing quantum operations or channels, if they exist, that transform a given set of quantum states $\{\rho_1, \dots, \rho_k\}$ to another such set $\{\hat\rho_1, \dots, \hat\rho_k\}$. In other words, we must…
We consider the distributionally robust optimization and show that computing the distributional worst-case is equivalent to computing the projection onto the canonical simplex with additional linear inequality. We consider several distance…
We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex…
We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…