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We analyze two classical algorithms for solving additively composite convex optimization problems where the objective is the sum of a smooth term and a nonsmooth regularizer: proximal stochastic gradient method for a single regularizer; and…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
Complexity of the Operations Research Theory tasks can be often diminished in cases that do not require finding the exact solution. For example, forecasting two-dimensional hierarchical time series leads us to the transportation problem…
A probabilistic approach of computing geometric rate of convergence of stochastic processes is introduced in this paper. The goal is to quantitatively compute both upper and lower bounds of the exponential rate of convergence to the…
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…
Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…
Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such…
In this paper, we compute quadratic rates of asymptotic regularity for the Tikhonov-Mann iteration in W-hyperbolic spaces. This iteration is an extension to a nonlinear setting of the modified Mann iteration defined recently by Bot, Csetnek…
We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
We propose a successive generation of cutting inequalities for binary quadratic optimization problems. Multiple cutting inequalities are successively generated for the convex hull of the set of the optimal solutions $\subset \{0, 1\}^n$,…
Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…
In this paper, a proof of asymptotic stability for the combined system-optimizer dynamics associated with a class of real-time methods for equality constrained nonlinear model predictive control is presented. General Q-linearly convergent…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
Iterative hard thresholding (IHT) has gained in popularity over the past decades in large-scale optimization. However, convergence properties of this method have only been explored recently in non-convex settings. In matrix completion,…
We establish the uniform in time stability, w.r.t. the marginals, of the Iterative Proportional Fitting Procedure, also known as Sinkhorn algorithm, used to solve entropy-regularised Optimal Transport problems. Our result is quantitative…
Machine learning practitioners invest significant manual and computational resources in finding suitable learning rates for optimization algorithms. We provide a probabilistic motivation, in terms of Gaussian inference, for popular…
In this paper we obtain a quadratic bound on the rate of asymptotic regularity for the Krasnoselski-Mann iterations of nonexpansive mappings in CAT(0)-spaces, whereas previous results guarantee only exponential bounds. The method we use is…