Related papers: A Unified Approach to Error Bounds for Structured …

In this paper, we provide the universal first-order methods of Composite Optimization with new complexity analysis. It delivers some universal convergence guarantees, which are not linked directly to any parametric problem class. However,…

This paper considers online convex optimization with long term constraints, where constraints can be violated in intermediate rounds, but need to be satisfied in the long run. The cumulative constraint violation is used as the metric to…

Consider reconstructing a signal $x$ by minimizing a weighted sum of a convex differentiable negative log-likelihood (NLL) (data-fidelity) term and a convex regularization term that imposes a convex-set constraint on $x$ and enforces its…

Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…

We consider minimization problems with structured objective function and smooth constraints, and present a flexible framework that combines the beneficial regularization effects of (exact) penalty and interior-point methods. In the fully…

This paper proposes a framework to study the convergence of stochastic optimization and learning algorithms. The framework is modeled over the different challenges that these algorithms pose, such as (i) the presence of random additive…

Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…

We consider the problem of synthesizing optimal linear feedback policies subject to arbitrary convex constraints on the feedback matrix. This is known to be a hard problem in the usual formulations ($\Htwo,\Hinf,\LQR$) and previous works…

We consider a class of stochastic gradient optimization schemes. Assuming that the objective function is strongly convex, we prove weak error estimates which are uniform in time for the error between the solution of the numerical scheme,…

We consider the problem of stochastic convex optimization with exp-concave losses using Empirical Risk Minimization in a convex class. Answering a question raised in several prior works, we provide a $O( d / n + \log( 1 / \delta) / n )$…

In the last several years, the intimate connection between convex optimization and learning problems, in both statistical and sequential frameworks, has shifted the focus of algorithmic machine learning to examine this interplay. In…

Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate…

The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…

Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a…

Convex relaxations are effective for training and certifying neural networks against norm-bounded adversarial attacks, but they leave a large gap between certifiable and empirical robustness. In principle, convex relaxation can provide…

We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…

We provide a framework for obtaining error bounds for linear conic problems without assuming constraint qualifications or regularity conditions. The key aspects of our approach are the notions of amenable cones and facial residual…

Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…

Time series forecasting has become a critical task due to its high practicality in real-world applications such as traffic, energy consumption, economics and finance, and disease analysis. Recent deep-learning-based approaches have shown…

In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. To…