Related papers: Solving rank-constrained semidefinite programs in …
We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum polynomial game in randomized…
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…
We consider the decision problem asking whether a partial rational symmetric matrix with an all-ones diagonal can be completed to a full positive semidefinite matrix of rank at most $k$. We show that this problem is $\NP$-hard for any fixed…
We develop a practical semidefinite programming (SDP) facial reduction procedure that utilizes computationally efficient approximations of the positive semidefinite cone. The proposed method simplifies SDPs with no strictly feasible…
The problem of minimizing the rank of a symmetric positive semidefinite matrix subject to constraints can be cast equivalently as a semidefinite program with complementarity constraints (SDCMPCC). The formulation requires two positive…
The Quadratic Assignment Problem (QAP) is an important discrete optimization instance that encompasses many well-known combinatorial optimization problems, and has applications in a wide range of areas such as logistics and computer vision.…
In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…
In this paper, we study possible extensions of the main ideas and methods of constrained DC optimization to the case of nonlinear semidefinite programming problems and more general nonlinear and nonsmooth cone constrained optimization…
Rank regularized minimization problem is an ideal model for the low-rank matrix completion/recovery problem. The matrix factorization approach can transform the high-dimensional rank regularized problem to a low-dimensional factorized…
We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a…
The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, a drawback of the known approaches is that the rank parameter has to be fixed a priori. In this paper, we consider the…
We consider the solution of nonlinear programs with nonlinear semidefiniteness constraints. The need for an efficient exploitation of the cone of positive semidefinite matrices makes the solution of such nonlinear semidefinite programs more…
We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important…
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…
The problem of optimizing over the cone of nonnegative polynomials is a fundamental problem in computational mathematics, with applications to polynomial optimization, control, machine learning, game theory, and combinatorics, among others.…
This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and…
This paper presents generalizations of semidefinite programming formulations of 1-norm optimization problems over infinite dictionaries of vectors of complex exponentials, which were recently proposed for superresolution, gridless…
Minimizing the rank of a matrix subject to constraints is a challenging problem that arises in many applications in control theory, machine learning, and discrete geometry. This class of optimization problems, known as rank minimization, is…
Finding whether a linear-constraint loop has a linear ranking function is an important key to understanding the loop behavior, proving its termination and establishing iteration bounds. If no preconditions are provided, the decision problem…
An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained…