Related papers: Rescaling Algorithms for Linear Conic Feasibility

We propose a new first-order augmented Lagrangian algorithm ALCC for solving convex conic programs of the form min{rho(x)+gamma(x): Ax-b in K, x in chi}, where rho and gamma are closed convex functions, and gamma has a Lipschitz continuous…

We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension $d$: i) Given $n$ points in $\Rd$, compute their minimum enclosing cylinder. ii) Given two $n$-point sets in $\Rd$, decide…

We study the possibility of designing $N^{o(1)}$-round protocols for problems of substantially super-linear polynomial-time (sequential) complexity in the model of Massively Parallel Computation, where $N$ is the input size. We show that if…

Integer programs with m constraints are solvable in pseudo-polynomial time in $\Delta$, the largest coefficient in a constraint, when m is a fixed constant. We give a new algorithm with a running time of $O(\sqrt{m}\Delta)^{2m} + O(nm)$,…

This paper deals with the numerical computation of the least singular value of a rectangular matrix $A$ relative to a pair of closed convex cones $(P,Q)$, which is defined as the optimal value of the non-convex optimization problem of…

In this paper, we propose an arc-search infeasible-interior-point algorithm. We show that this algorithm is polynomial and the polynomial bound is ${\cal O}(nL)$ which is at least as good as the best existing bound for…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

It is well-known that spatial averaging can be realized (in space or frequency domain) using algorithms whose complexity does not depend on the size or shape of the filter. These fast algorithms are generally referred to as constant-time or…

Interior Point Methods are widely used to solve Linear Programming problems. In this work, we present two primal affine scaling algorithms to achieve faster convergence in solving Linear Programming problems. In the first algorithm, we…

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 propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive…

We consider interactive learning in the realizable setting and develop a general framework to handle problems ranging from best arm identification to active classification. We begin our investigation with the observation that agnostic…

It has been observed in many places that constant-factor approximable problems often admit polynomial or even linear problem kernels for their decision versions, e.g., Vertex Cover, Feedback Vertex Set, and Triangle Packing. While there…

In spatial statistics and machine learning, the kernel matrix plays a pivotal role in prediction, classification, and maximum likelihood estimation. A thorough examination reveals that for large sample sizes, the kernel matrix becomes…

The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…

We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…

This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…

We study the L1 minimization problem with additional box constraints. We motivate the problem with two different views of optimality considerations. We look into imposing such constraints in projected gradient techniques and propose a worst…

Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is…

A wide range of fundamental machine learning tasks that are addressed by the maximum a posteriori estimation can be reduced to a general minimum conical hull problem. The best-known solution to tackle general minimum conical hull problems…