Related papers: Tight SDP relaxations for cardinality-constrained …
Semidefinite programs are convex optimisation problems involving a linear objective function and a domain of positive semidefinite matrices. Over the last two decades, they have become an indispensable tool in quantum information science.…
We consider optimization problems containing nonconvex quadratic functions for which semidefinite programming (SDP) relaxations often yield strong bounds. We investigate linear inequalities that outer approximate the positive semidefinite…
Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that…
In this paper, by improving the variable-splitting approach, we propose a new semidefinite programming (SDP) relaxation for the nonconvex quadratic optimization problem over the $\ell_1$ unit ball (QPL1). It dominates the state-of-the-art…
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial…
While semidefinite programming (SDP) problems are polynomially solvable in theory, it is often difficult to solve large SDP instances in practice. One technique to address this issue is to relax the global positive-semidefiniteness (PSD)…
We present a new generic approach to the condensed-matter ground-state problem which is complementary to variational techniques and works directly in the thermodynamic limit. Relaxing the ground-state problem, we obtain semidefinite…
In this paper we study the relationship between the optimal value of a homogeneous quadratic optimization problem and that of its Semidefinite Programming (SDP) relaxation. We consider two quadratic optimization models: (1) $\min \{x^* C x…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable…
Why is it that semidefinite relaxations have been so successful in numerous applications in computer vision and robotics for solving non-convex optimization problems involving rotations? In studying the empirical performance we note that…
A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the…
We study the exactness of the semidefinite programming (SDP) relaxation of quadratically constrained quadratic programs (QCQPs). With the aggregate sparsity matrix from the data matrices of a QCQP with $n$ variables, the rank and positive…
This paper formulates a semidefinite programming relaxation for a long horizon direct-torque finite-control-set model predictive control problem. In parallel with this relaxation, a conventional branch-and-bound algorithm tailored for the…
We consider a new semidefinite programming (SDP) relaxation of the symmetric traveling salesman problem (TSP) that may be obtained via an SDP relaxation of the more general quadratic assignment problem (QAP). We show that the new relaxation…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
We discuss how semidefinite programming can be used to determine the second-order density matrix directly through a variational optimization. We show how the problem of characterizing a physical or N -representable density matrix leads to…
Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…
Semidefinite programming (SDP) problems are challenging to solve because of their high dimensionality. However, solving sparse SDP problems with small tree-width are known to be relatively easier because: (1) they can be decomposed into…
The cardinality-constrained mean-variance portfolio problem has garnered significant attention within contemporary finance due to its potential for achieving low risk while effectively managing risks and transaction costs. Instead of…