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We propose a new generative model for layout generation. We generate layouts in three steps. First, we generate the layout elements as nodes in a layout graph. Second, we compute constraints between layout elements as edges in the layout…
Stochastic gradient method (SGM) has been popularly applied to solve optimization problems with objective that is stochastic or an average of many functions. Most existing works on SGMs assume that the underlying problem is unconstrained or…
We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…
In this work, we develop a control-theoretic framework for constrained optimization problems with composite objective functions including non-differentiable terms. Building on the proximal augmented Lagrangian formulation, we construct a…
Ising machines are expected to solve combinatorial optimization problems faster than the existing integer programming solvers. These problems, particularly those encountered in practical situations, typically involve inequality constraints.…
We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…
This work investigates the convergence behavior of augmented Lagrangian methods (ALMs) when applied to convex optimization problems that may be infeasible. ALMs are a popular class of algorithms for solving constrained optimization…
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…
We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…
We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…
A broad class of optimization problems can be cast in composite form, that is, considering the minimization of the composition of a lower semicontinuous function with a differentiable mapping. This paper investigates the versatile template…
Compressing neural nets is an active research problem, given the large size of state-of-the-art nets for tasks such as object recognition, and the computational limits imposed by mobile devices. We give a general formulation of model…
Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential applications in risk-averse machine learning, semisupervised learning, and robust optimization…
This paper studies the estimation of ranked-list discrete choice models with single and multiple purchases. In this setting, each consumer type is characterized by a ranking over a subset of products and a desired number of purchases, and…
Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…
In this paper we provide a detailed analysis of the iteration complexity of dual first order methods for solving conic convex problems. When it is difficult to project on the primal feasible set described by convex constraints, we use the…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…
We introduce a novel approach addressing global analysis of a difficult class of nonconvex-nonsmooth optimization problems within the important framework of Lagrangian-based methods. This genuine nonlinear class captures many problems in…
This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization…