Related papers: Stochastic Monotone Inclusion with Closed Loop Dis…
We propose a novel approach to monotone operator splitting based on the notion of a saddle operator. Under investigation is a highly structured multivariate monotone inclusion problem involving a mix of set-valued, cocoercive, and…
We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…
Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost…
The paper studies the robustness properties of discrete-time stochastic optimal control under Wasserstein model approximation for both discounted-cost and average-cost criteria. Specifically, we study the performance loss when applying an…
We consider monotone inclusions defined on a Hilbert space where the operator is given by the sum of a maximal monotone operator $T$ and a single-valued monotone, Lipschitz continuous, and expectation-valued operator $V$. We draw motivation…
In this paper we investigate the convergence behavior of a primal-dual splitting method for solving monotone inclusions involving mixtures of composite, Lipschitzian and parallel sum type operators proposed by Combettes and Pesquet in [7].…
To address the issue of inaccurate distributions in practical stochastic systems, a minimax linear-quadratic control method is proposed using the Wasserstein metric. Our method aims to construct a control policy that is robust against…
This paper thoroughly investigates stochastic linear-quadratic optimal control problems with the Markovian regime switching system, where the coefficients of the state equation and the weighting matrices of the cost functional are random.…
In this paper, we introduce three novel splitting algorithms for solving structured monotone inclusion problems involving the sum of a maximally monotone operator, a monotone and Lipschitz continuous operator and a cocoercive operator. Each…
We consider the basic problem of learning Single-Index Models with respect to the square loss under the Gaussian distribution in the presence of adversarial label noise. Our main contribution is the first computationally efficient algorithm…
This paper studies a class of multiagent stochastic optimization problems where the objective is to minimize the expected value of a function which depends on a random variable. The probability distribution of the random variable is unknown…
We consider stochastic optimization problems involving an expected value of a nonlinear function of a base random vector and a conditional expectation of another function depending on the base random vector, a dependent random vector, and…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
This paper concerns state constrained optimal control problems, in which the dynamic constraint takes the form of a differential inclusion. If the differential inclusion does not depend on time, then the Hamiltonian, evaluated along the…
Distributionally robust stochastic optimization (DRSO) is a framework for decision-making problems under certainty, which finds solutions that perform well for a chosen set of probability distributions. Many different approaches for…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
In this work, we consider the distributed optimization of non-smooth convex functions using a network of computing units. We investigate this problem under two regularity assumptions: (1) the Lipschitz continuity of the global objective…
This book is devoted to finite-dimensional problems of non-convex non-smooth optimization and numerical methods for their solution. The problem of nonconvexity is studied in the book on two main models of nonconvex dependencies: these are…
We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but whose joint distribution is not. We establish and exploit an…
In the framework of a real Hilbert space, we address the problem of finding the zeros of the sum of a maximally monotone operator $A$ and a cocoercive operator $B$. We study the asymptotic behaviour of the trajectories generated by a second…