Related papers: Several classes of stationary points for rank regu…
This paper studies the problem of deterministic rank-one matrix completion. It is known that the simplest semidefinite programming relaxation, involving minimization of the nuclear norm, does not in general return the solution for this…
We present an analysis of sets of matrices with rank less than or equal to a specified number $s$. We provide a simple formula for the normal cone to such sets, and use this to show that these sets are prox-regular at all points with rank…
This paper studies a discrete-time major-minor mean field game of stopping where the major player can choose either an optimal control or stopping time. We look for the relaxed equilibrium as a randomized stopping policy, which is…
The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in…
Low rank regularization, in essence, involves introducing a low rank or approximately low rank assumption for matrix we aim to learn, which has achieved great success in many fields including machine learning, data mining and computer…
A mathematical programming problem with affine equilibrium constraints (AMPEC) is a bilevel programming problem where the lower one is a parametric affine variational inequality. We formulate some classes of bilevel programming in forms of…
Matrix rank minimization problems are gaining a plenty of recent attention in both mathematical and engineering fields. This class of problems, arising in various and across-discipline applications, is known to be NP-hard in general. In…
We show that a class of semidefinite programs (SDP) admits a solution that is a positive semidefinite matrix of rank at most $r$, where $r$ is the rank of the matrix involved in the objective function of the SDP. The optimization problems…
Estimating equations arise in a wide range of statistical applications, including longitudinal and clustered data analysis, survival analysis, econometrics, and semiparametric inference. In high-dimensional settings, adding…
Optimization with nonnegative orthogonality constraints has wide applications in machine learning and data sciences. It is NP-hard due to some combinatorial properties of the constraints. We first propose an equivalent optimization…
This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in…
The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eight-point algorithm and two-view projective bundle adjustment. The eight-point algorithm first computes a simple linear least…
Solving the explicit Model Predictive Control (MPC) problem requires enumerating all critical regions and their associated feedback laws, a task that scales exponentially with the system dimension and the prediction horizon, as well. When…
Common computational problems, such as parameter estimation in dynamic models and PDE constrained optimization, require data fitting over a set of auxiliary parameters subject to physical constraints over an underlying state. Naive…
Provably finding stationary points on bounded-rank tensors turns out to be an open problem [E. Levin, J. Kileel, and N. Boumal, Math. Program., 199 (2023), pp. 831--864] due to the inherent non-smoothness of the set of bounded-rank tensors.…
In this paper, we study properties of penalized and structured M-estimators of multivariate scatter, based on geodesically convex but not necessarily smooth penalty functions. Existence and uniqueness conditions for these penalized and…
We introduce new first-order necessary conditions for mathematical programs with complementarity constraints (MPCCs), which lie between strong and M-stationarity and have a relatively simple description. We show that they hold for local…
This paper focuses on the study of a mathematical program with equilibrium constraints, where the objective and the constraint functions are all polynomials. We present a method for finding its global minimizers and global minimum using a…
This paper focuses on the error bounds for several equivalent rank-one doubly nonnegative (DNN) conic reformulations of the quadratic assignment problem (QAP), a class of challenging combinatorial optimization problems. We provide three…
This paper introduces and studies the optimal control problem with equilibrium constraints (OCPEC). The OCPEC is an optimal control problem with a mixed state and control equilibrium constraint formulated as a complementarity constraint and…