Related papers: Sequential constant rank constraint qualifications…

We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…

Semidefinite programming (SDP) is a unifying framework that generalizes both linear programming and quadratically-constrained quadratic programming, while also yielding efficient solvers, both in theory and in practice. However, there exist…

We show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order $1$),…

We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

In this paper, we propose a method that has foundations in the line search sequential quadratic programming paradigm for solving general nonlinear equality constrained optimization problems. The method employs a carefully designed modified…

The literature on stochastic programming typically restricts attention to problems that fulfill constraint qualifications. The literature on estimation and inference under partial identification frequently restricts the geometry of…

Since more than three decades, interior-point methods proved very useful for optimization, from linear over semidefinite to conic (and partly beyond non-convex) programming; despite the fact that already in the semidefinite case (even when…

Many problems in information theory can be reduced to optimizations over matrices, where the rank of the matrices is constrained. We establish a link between rank-constrained optimization and the theory of quantum entanglement. More…

Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…

We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point…

Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In…

This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the…

In this paper, we consider a large class of nonlinear equations derived from first-order type methods for solving composite optimization problems. Traditional approaches to establishing superlinear convergence rates of semismooth…

This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…

This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum…

Many classical and modern machine learning algorithms require solving optimization tasks under orthogonality constraints. Solving these tasks with feasible methods requires a gradient descent update followed by a retraction operation on the…

We introduce constraints necessary for type checking a higher-order concurrent constraint language, and solve them with an incremental algorithm. Our constraint system extends rational unification by constraints x$\subseteq$ y saying that…

A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…

In this paper, we study the difficult class of optimization problems called the mathematical programs with vanishing constraints or MPVC. Extensive research has been done for MPVC regarding stationary conditions and constraint…