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Arising in semi-parametric statistics, control applications, and as sub-problems in global optimization methods, certain optimization problems can have objective functions requiring numerical integration to evaluate, yet gradient function…
This paper considers a class of convex optimization problems where both, the objective function and the constraints, have a continuously varying dependence on time. Our goal is to develop an algorithm to track the optimal solution as it…
In this paper, we analyze the convergence of several discretize-then-optimize algorithms, based on either a second-order or a fourth-order finite difference discretization, for solving elliptic PDE-constrained optimization or optimal…
This paper is devoted to the distributed continuous-time optimization problem with time-varying objective functions and time-varying nonlinear inequality constraints. Different from most studied distributed optimization problems with…
This paper considers the problem of decentralized optimization on compact submanifolds, where a finite sum of smooth (possibly non-convex) local functions is minimized by $n$ agents forming an undirected and connected graph. However, the…
This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the…
Decentralized optimization enables multiple devices to learn a global machine learning model while each individual device only has access to its local dataset. By avoiding the need for training data to leave individual users' devices, it…
Minimax problems have recently attracted a lot of research interests. A few efforts have been made to solve decentralized nonconvex strongly-concave (NCSC) minimax-structured optimization; however, all of them focus on smooth problems with…
In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain…
This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…
We consider constraint-coupled optimization problems in which agents of a network aim to cooperatively minimize the sum of local objective functions subject to individual constraints and a common linear coupling constraint. We propose a…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
Many large-scale constrained optimization problems can be formulated as bilevel distributed optimization tasks over undirected networks, where agents collaborate to minimize a global cost function while adhering to constraints, relying only…
A conventional way to handle model predictive control (MPC) problems distributedly is to solve them via dual decomposition and gradient ascent. However, at each time-step, it might not be feasible to wait for the dual algorithm to converge.…
Concerning huge-scale aggregative convex programming of a linear objective subject to the affine constraints of equality and inequality and the quadratic constraints of inequality, convex and aggregatively computable, an algorithm is…
In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…
We consider distributed online convex optimization problems, where the distributed system consists of various computing units connected through a time-varying communication graph. In each time step, each computing unit selects a constrained…
In the distributed optimization problem for a multi-agent system, each agent knows a local function and must find a minimizer of the sum of all agents' local functions by performing a combination of local gradient evaluations and…
To design algorithms that reduce communication cost or meet rate constraints and are robust to communication noise, we study convex distributed optimization problems where a set of agents are interested in solving a separable optimization…