Related papers: Dual Interior Point Optimization Learning
In this paper we provide an algorithm for solving constrained composite primal-dual monotone inclusions, i.e., monotone inclusions in which a priori information on primal-dual solutions is represented via closed convex sets. The proposed…
When solving optimization problems under uncertainty with contextual data, utilizing machine learning to predict the uncertain parameters' values is a popular and effective approach. Decision-focused learning (DFL) aims at learning a…
In this paper, we develop an interior-point method for solving a class of convex optimization problems with time-varying objective and constraint functions. Using log-barrier penalty functions, we propose a continuous-time dynamical system…
The minimization of convex objectives coming from linear supervised learning problems, such as penalized generalized linear models, can be formulated as finite sums of convex functions. For such problems, a large set of stochastic…
With the unprecedented growth of signal processing and machine learning application domains, there has been a tremendous expansion of interest in distributed optimization methods to cope with the underlying large-scale problems.…
Linear programming has been practically solved mainly by simplex and interior point methods. Compared with the weakly polynomial complexity obtained by the interior point methods, the existence of strongly polynomial bounds for the length…
Creating impact in real-world settings requires artificial intelligence techniques to span the full pipeline from data, to predictive models, to decisions. These components are typically approached separately: a machine learning model is…
We propose a modified primal-dual method for general convex optimization problems with changing constraints. We obtain properties of Lagrangian saddle points for these problems which enable us to establish convergence of the proposed…
Dual averaging-type methods are widely used in industrial machine learning applications due to their ability to promoting solution structure (e.g., sparsity) efficiently. In this paper, we propose a novel accelerated dual-averaging…
In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step…
Model training algorithms which observe a small portion of the training set in each computational step are ubiquitous in practical machine learning, and include both stochastic and online optimization methods. In the vast majority of cases,…
We review the simplex method and two interior-point methods (the affine scaling and the primal-dual) for solving linear programming problems for checking avoiding sure loss, and propose novel improvements. We exploit the structure of these…
In this paper we provide a detailed analysis of the iteration complexity of dual first order methods for solving conic convex problems. When it is difficult to project on the primal feasible set described by convex constraints, we use the…
Many real-world decision processes are modeled by optimization problems whose defining parameters are unknown and must be inferred from observable data. The Predict-Then-Optimize framework uses machine learning models to predict unknown…
We design accelerated algorithms with improved rates for several fundamental classes of optimization problems. Our algorithms all build upon techniques related to the analysis of primal-dual extragradient methods via relative Lipschitzness…
We propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications. Our optimization algorithms feature optimal convergence guarantees under a variety of common structure assumptions…
Learning to Optimize (LtO) is a problem setting in which a machine learning (ML) model is trained to emulate a constrained optimization solver. Learning to produce optimal and feasible solutions subject to complex constraints is a difficult…
In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…
We propose a new methodology for parameterized constrained robust optimization, an important class of optimization problems under uncertainty, based on learning with a self-supervised penalty-based loss function. Whereas supervised learning…
The topic of learning to solve optimization problems has received interest from both the operations research and machine learning communities. In this work, we combine techniques from both fields to address the problem of learning to…