quadratic penalty – Optimization Online

Variance-reduced first-order methods for deterministically constrained stochastic nonconvex optimization with strong convergence guarantees

Published: 2024/09/15, Updated: 2024/10/10

Constrained Nonlinear Optimization, Stochastic Programming Polyak momentum, quadratic penalty, recursive momentum, sample complexity, stochastic optimization, variance reduction

In this paper, we study a class of deterministically constrained stochastic optimization problems. Existing methods typically aim to find an \(\epsilon\)-stochastic stationary point, where the expected violations of both constraints and first-order stationarity are within a prescribed accuracy \(\epsilon\). However, in many practical applications, it is crucial that the constraints be nearly satisfied with certainty, … Read more

Regularized monotonic regression

Published: 2016/06/30

Oleg Burdakov

Oleg Sysoev

Quadratic Programming, Statistics convex quadratic programming, dual active-set method, large-scale optimization, monotonic regression, quadratic penalty, regularization

Monotonic (isotonic) Regression (MR) is a powerful tool used for solving a wide range of important applied problems. One of its features, which poses a limitation on its use in some areas, is that it produces a piecewise constant fitted response. For smoothing the fitted response, we introduce a regularization term in the MR formulated … Read more