Related papers: About the Complexity of Two-Stage Stochastic IPs
In this paper, a two-step strategy for parametric sensitivity analysis for such systems is proposed, exploiting advantages and synergies between two recently proposed sensitivity analysis methodologies for stochastic dynamics. The first…
It is common practice to apply gradient-based optimization algorithms to numerically solve large-scale ODE constrained optimal control problems. Gradients of the objective function are most efficiently computed by approximate adjoint…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
We address high-dimensional zero-one random parameters in two-stage convex conic optimization problems. Such parameters typically represent failures of network elements and constitute rare, high-impact random events in several applications.…
Sparse coding is typically solved by iterative optimization techniques, such as the Iterative Shrinkage-Thresholding Algorithm (ISTA). Unfolding and learning weights of ISTA using neural networks is a practical way to accelerate estimation.…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
Multi-stage decision-making under uncertainty, where decisions are taken under sequentially revealing uncertain problem parameters, is often essential to faithfully model managerial problems. Given the significant computational challenges…
Stochastic gradient descent (SGD) is one of the most widely used algorithms for large scale optimization problems. While classical theoretical analysis of SGD for convex problems studies (suffix) \emph{averages} of iterates and obtains…
Stochastic approximation (SA) and stochastic gradient descent (SGD) algorithms are work-horses for modern machine learning algorithms. Their constant stepsize variants are preferred in practice due to fast convergence behavior. However,…
Iterative Hard Thresholding (IHT) is a class of projected gradient descent methods for optimizing sparsity-constrained minimization models, with the best known efficiency and scalability in practice. As far as we know, the existing…
A novel approach termed \emph{stochastic truncated amplitude flow} (STAF) is developed to reconstruct an unknown $n$-dimensional real-/complex-valued signal $\bm{x}$ from $m$ `phaseless' quadratic equations of the form…
We show a new way to round vector solutions of semidefinite programming (SDP) hierarchies into integral solutions, based on a connection between these hierarchies and the spectrum of the input graph. We demonstrate the utility of our method…
The Densest Subgraph Problem (DSP) is widely used to identify community structures and patterns in networks such as bioinformatics and social networks. While solvable in polynomial time, traditional exact algorithms face computational and…
Recently a majorization method for optimizing partition functions of log-linear models was proposed alongside a novel quadratic variational upper-bound. In the batch setting, it outperformed state-of-the-art first- and second-order…
We consider two-stage robust optimization problems, which can be seen as games between a decision maker and an adversary. After the decision maker fixes part of the solution, the adversary chooses a scenario from a specified uncertainty…
We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general…
We consider (stochastic) convex-concave saddle point (SP) problems with high-dimensional decision variables, arising in various applications including machine learning problems. To contend with the challenges in computing full gradients, we…
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…