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Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
This paper proposes model reduction approaches for consensus network systems based on a given clustering of the underlying graph. Namely, given a consensus network system of time-scaled agents evolving over a weighted undirected graph and a…
We consider the general problem of minimizing an objective function which is the sum of a convex function (not strictly convex) and absolute values of a subset of variables (or equivalently the l1-norm of the variables). This problem…
Consensus based optimization (CBO) employs a swarm of particles evolving as a system of stochastic differential equations (SDEs). Recently, it has been adapted to yield a derivative free sampling method referred to as consensus based…
We study the convergence of the Augmented Decomposition Algorithm (ADA) proposed in [32] for solving multi-block separable convex minimization problems subject to linear constraints. We show that the global convergence rate of the exact ADA…
Proximal policy optimization and trust region policy optimization (PPO and TRPO) with actor and critic parametrized by neural networks achieve significant empirical success in deep reinforcement learning. However, due to nonconvexity, the…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
For obtaining optimal first-order convergence guarantee for stochastic optimization, it is necessary to use a recurrent data sampling algorithm that samples every data point with sufficient frequency. Most commonly used data sampling…
This paper investigates the asymptotic convergence behavior of high-order proximal-point algorithms (HiPPA) toward global minimizers, extending the analysis beyond sublinear convergence rate results. Specifically, we consider the proximal…
Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple…
Black-box zero-th order optimization is a central primitive for applications in fields as diverse as finance, physics, and engineering. In a common formulation of this problem, a designer sequentially attempts candidate solutions, receiving…
We propose a globally convergent trust-region bundle method for minimizing lower-$C^2$ functions using higher-order cutting-plane models. Under certain growth assumptions on the objective around its minimum, the method is able to compute…
This paper deals with an inertial proximal algorithm that contains a Tikhonov regularization term, in connection to the minimization problem of a convex lower semicontinuous function $f$. We show that for appropriate Tikhonov regularization…
We address an optimization problem where the cost function is the expectation of a random mapping. To tackle the problem two approaches based on the approximation of the objective function by consensus-based particle optimization methods on…
We propose and analyze asymptotic proximal point (APP) methods to find the global minimizer for a class of nonconvex, nonsmooth, or even discontinuous multiple minima functions. The method is based on an asymptotic representation of…
We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…
Gaussian process (GP) based Bayesian optimization (BO) is a powerful method for optimizing black-box functions efficiently. The practical performance and theoretical guarantees of this approach depend on having the correct GP hyperparameter…
Stochastic optimization finds a wide range of applications in operations research and management science. However, existing stochastic optimization techniques usually require the information of random samples (e.g., demands in the…
Most off-policy evaluation methods for contextual bandits have focused on the expected outcome of a policy, which is estimated via methods that at best provide only asymptotic guarantees. However, in many applications, the expectation may…
This paper proposes a theoretical framework of the grey wolf optimizer (GWO) based on several interesting theoretical findings, involving sampling distribution, order-1 and order-2 stability, and global convergence analysis. In the part II…