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Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…

We consider the general problem of minimizing an objective function which is the sum of a convex function (not strictly convex) and absolute values of a subset of variables (or equivalently the l1-norm of the variables). This problem…

Submodular functions are an important class of functions in combinatorial optimization which satisfy the natural properties of decreasing marginal costs. The study of these functions has led to strong structural properties with applications…

Mini-batch gradient descent based methods are the de facto algorithms for training neural network architectures today. We introduce a mini-batch selection strategy based on submodular function maximization. Our novel submodular formulation…

Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the…

Submodular functions are at the core of many machine learning and data mining tasks. The underlying submodular functions for many of these tasks are decomposable, i.e., they are sum of several simple submodular functions. In many data…

Many computer vision problems (e.g., camera calibration, image alignment, structure from motion) are solved with nonlinear optimization methods. It is generally accepted that second order descent methods are the most robust, fast, and…

In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…

The block coordinate descent (BCD) method is widely used for minimizing a continuous function f of several block variables. At each iteration of this method, a single block of variables is optimized, while the remaining variables are held…

In this paper some adaptive mirror descent algorithms for problems of minimization convex objective functional with several convex Lipschitz (generally, non-smooth) functional constraints are considered. It is shown that the methods are…

Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…

We study the problem of minimizing the sum of a smooth convex function and a convex block-separable regularizer and propose a new randomized coordinate descent method, which we call ALPHA. Our method at every iteration updates a random…

Robust Optimization is becoming increasingly important in machine learning applications. This paper studies the problem of robust submodular minimization subject to combinatorial constraints. Constrained Submodular Minimization arises in…

In this paper, we study randomized and cyclic coordinate descent for convex unconstrained optimization problems. We improve the known convergence rates in some cases by using the numerical semidefinite programming performance estimation…

Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…

We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…

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 describe an asynchronous parallel stochastic proximal coordinate descent algorithm for minimizing a composite objective function, which consists of a smooth convex function plus a separable convex function. In contrast to previous…

In this paper, a sequential search method for finding the global minimum of an objective function is presented, The descent gradient search is repeated until the global minimum is obtained. The global minimum is located by a process of…

We propose a method for analyzing the distributed random coordinate descent algorithm for solving separable resource allocation problems in the context of an open multiagent system, where agents can be replaced during the process. In…