Related papers: Rank-Constrained Schur-Convex Optimization with Mu…
We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function,…
This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain of the optimization variable, which are difficult to project onto; and (b) deterministic or stochastic…
In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…
We consider the optimization problem of minimizing the sum-of-nonconvex function, i.e., a convex function that is the average of nonconvex components. The existing stochastic algorithms for such a problem only focus on a single machine and…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…
We study quasi-convex optimization problems, where only a subset of the constraints can be sampled, and yet one would like a probabilistic guarantee on the obtained solution with respect to the initial (unknown) optimization problem. Even…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…
The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a global optimal solution can be computed with a branch-and-bound method, it is very…
In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…
We propose a regularized saddle-point algorithm for convex networked optimization problems with resource allocation constraints. Standard distributed gradient methods suffer from slow convergence and require excessive communication when…
Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
This paper presents an algorithm to solve non-convex optimal control problems, where non-convexity can arise from nonlinear dynamics, and non-convex state and control constraints. This paper assumes that the state and control constraints…
Many nonconvex problems in robotics can be relaxed into convex formulations via Semi-Definite Programming (SDP) that can be solved to global optimality. The practical quality of these solutions, however, critically depends on rounding them…
Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…
A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few…
Convex optimization problems with staged structure appear in several contexts, including optimal control, verification of deep neural networks, and isotonic regression. Off-the-shelf solvers can solve these problems but may scale poorly. We…
Two common approaches in low-rank optimization problems are either working directly with a rank constraint on the matrix variable, or optimizing over a low-rank factorization so that the rank constraint is implicitly ensured. In this paper,…
Min-max optimization is emerging as a key framework for analyzing problems of robustness to strategically and adversarially generated data. We propose a random reshuffling-based gradient free Optimistic Gradient Descent-Ascent algorithm for…