Related papers: Efficient Computation of Integer-constrained Cones…

Many existing branch and bound algorithms for multiobjective optimization problems require a significant computational cost to approximate the entire Pareto optimal solution set. In this paper, we propose a new branch and bound algorithm…

Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…

We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…

We describe and analyze an interior-point method to decide feasibility problems of second-order conic systems. A main feature of our algorithm is that arithmetic operations are performed with finite precision. Bounds for both the number of…

This paper presents rigorous forward error bounds for linear conic optimization problems. The error bounds are formulated in a quite general framework; the underlying vector spaces are not required to be finite-dimensional, and the convex…

We address high-dimensional zero-one random parameters in two-stage convex conic optimization problems. Such parameters typically represent failures of network elements and constitute rare, high-impact random events in several applications.…

In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…

Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…

Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a…

The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…

In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…

This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a…

In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an $\epsilon$-accurate solution with probability at…

Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…

Motivated by the need for communication-efficient distributed learning, we investigate the method for compressing a unit norm vector into the minimum number of bits, while still allowing for some acceptable level of distortion in recovery.…

We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite…

Given real numbers whose sum is an integer, we study the problem of finding integers which match these real numbers as closely as possible, in the sense of L^p norm, while preserving the sum. We describe the structure of solutions for this…

In object segmentation by active contours, the initial contour is often required. Conventionally, the initial contour is provided by the user. This paper extends the conventional active contour model by incorporating feature matching in the…

Regression with sparse inputs is a common theme for large scale models. Optimizing the underlying linear algebra for sparse inputs allows such models to be estimated faster. At the same time, centering the inputs has benefits in improving…

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…