Related papers: Rate of metastability of an iterative algorithm fo…
A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…
We consider the rate of piecewise constant approximation to a locally stationary process $X(t),t\in [0,1]$, having a variable smoothness index $\alpha(t)$. Assuming that $\alpha(\cdot)$ attains its unique minimum at zero and satisfies the…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
We adapt the quasi-monotone method from [2] for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is…
In this paper we use proof mining methods to compute rates of ($T$-)asymptotic regularity of the generalized Krasnoselskii-Mann-type iteration associated to a nonexpansive mapping $T:X\to X$ in a uniformly convex normed space $X$. For…
We develop a quadratic regularization approach for the solution of high-dimensional multistage stochastic optimization problems characterized by a potentially large number of time periods/stages (e.g. hundreds), a high-dimensional resource…
We propose two distributed iterative algorithms that can be used to solve, in finite time, the distributed optimization problem over quadratic local cost functions in large-scale networks. The first algorithm exhibits synchronous operation…
Linear programs with quadratic regularization are attracting renewed interest due to their applications in optimal transport: unlike entropic regularization, the squared-norm penalty gives rise to sparse approximations of optimal transport…
In this paper, we solve a maximization problem where the objective function is quadratic and the constraints set is the reachable values set of a stable discrete-time affine system. This problem is equivalent to solve an infinite number of…
In combinatorial optimization, partial variable assignments are called persistent if they agree with some optimal solution. We propose persistency criteria for the multicut and max-cut problem as well as fast combinatorial routines to…
In the iterative algorithm recently proposed by Waxman for solving eigenvalue problems, we point out that the convergence rate may be improved. For many non-singular symmetric potentials which vanish asymptotically, a simple analytical…
We deal with the problem of the mean square optimal estimation of linear transformations of the unobserved values of a continuous time stochastic process with periodically correlated increments. Estimates are based on observations of the…
In this work, we state a general conjecture on the solvability of optimization problems via algorithms with linear convergence guarantees. We make a first step towards examining its correctness by fully characterizing the problems that are…
Quadratic assignment problem is one of the great challenges in combinatorial optimization. It has many applications in Operations research and Computer Science. In this paper, the author extends the most-used rounding approach to a…
In multivariate regression estimation, the rate of convergence depends on the dimension of the regressor. This fact, known as the curse of the dimensionality, motivated several works. The additive model, introduced by Stone (10), offers an…
This paper presents a probabilistic perspective on iterative methods for approximating the solution $\mathbf{x}_* \in \mathbb{R}^d$ of a nonsingular linear system $\mathbf{A} \mathbf{x}_* = \mathbf{b}$. In the approach a standard iterative…
We use techniques of proof mining to obtain a computable and uniform rate of metastability (in the sense of Tao) for the mean ergodic theorem for a finite number of commuting linear contractive operators on a uniformly convex Banach space.
We use techniques originating from the subdiscipline of mathematical logic called `proof mining' to provide rates of metastability and - under a metric regularity assumption - rates of convergence for a subgradient-type algorithm solving…
In practical applications of iterative first-order optimization, the learning rate schedule remains notoriously difficult to understand and expensive to tune. We demonstrate the presence of these subtleties even in the innocuous case when…