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This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees and practical performance. The method contains elements of two existing methods: the…
In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This interest surge is due to advancements in computing…
Recent advancements in data science have significantly elevated the importance of orthogonally constrained optimization problems. The Riemannian approach has become a popular technique for addressing these problems due to the advantageous…
This paper describes Convex, a convex optimization modeling framework in Julia. Convex translates problems from a user-friendly functional language into an abstract syntax tree describing the problem. This concise representation of the…
We study nonlinear optimization problems with a stochastic objective and deterministic equality and inequality constraints, which emerge in numerous applications including finance, manufacturing, power systems and, recently, deep neural…
We propose an inexact proximal augmented Lagrangian method (P-ALM) for nonconvex structured optimization problems. The proposed method features an easily implementable rule not only for updating the penalty parameters, but also for…
Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to…
The augmented Lagrangian method (ALM) is a benchmark for convex programming problems with linear constraints; ALM and its variants for linearly equality-constrained convex minimization models have been well studied in the literature.…
Most numerical methods developed for solving nonlinear programming problems are designed to find points that satisfy certain optimality conditions. While the Karush-Kuhn-Tucker conditions are well-known, they become invalid when constraint…
We present a derivative-based algorithm for nonlinearly constrained optimization problems that is tolerant of inaccuracies in the data. The algorithm solves a semi-smooth set of nonlinear equations that are equivalent to the first-order…
Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
Nonconvex mixed-integer nonlinear programs (MINLPs) represent a challenging class of optimization problems that often arise in engineering and scientific applications. Because of nonconvexities, these programs are typically solved with…
This paper presents a novel outer approximation algorithm for nonsmooth mixed-integer nonlinear programming (MINLP) problems. The method proceeds by fixing the integer variables and solving the resulting nonlinear convex subproblem. When…
Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…
Although unification can be used to implement a weak form of $\beta$-reduction, several linguistic phenomena are better handled by using some form of $\lambda$-calculus. In this paper we present a higher order feature description calculus…
This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal…
First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…
Recent developments in applied mathematics increasingly employ machine learning (ML)-particularly supervised learning-to accelerate numerical computations, such as solving nonlinear partial differential equations. In this work, we extend…
An adaptive regularization algorithm using high-order models is proposed for partially separable convexly constrained nonlinear optimization problems whose objective function contains non-Lipschitzian $\ell_q$-norm regularization terms for…