Related papers: An Enhanced SDR based Global Algorithm for Nonconv…
In Multiple-Input Multiple-Output (MIMO) systems, Sphere Decoding (SD) can achieve performance equivalent to full search Maximum Likelihood (ML) decoding, with reduced complexity. Several researchers reported techniques that reduce the…
In recent years there has been growing interest in study of multi-antenna transmit designs for providing secure communication over the physical layer. This paper considers the scenario of an intended multi-input single-output channel…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
In recent years, many estimation problems in robotics have been shown to be solvable to global optimality using their semidefinite relaxations. However, the runtime complexity of off-the-shelf semidefinite programming (SDP) solvers is up to…
This paper considers the (NP-)hard problem of joint multicast beamforming and antenna selection. Prior work has focused on using Semi-Definite relaxation (SDR) techniques in an attempt to obtain a high quality sub-optimal solution. However,…
We consider the detection of binary (antipodal) signals transmitted in a spatially multiplexed fashion over a fading multiple-input multiple-output (MIMO) channel and where the detection is done by means of semidefinite relaxation (SDR).…
We study optimization programs given by a bilinear form over non-commutative variables subject to linear inequalities. Problems of this form include the entangled value of two-prover games, entanglement-assisted coding for classical…
We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…
We aim to find a solution $\bm{x}\in\mathbb{C}^n$ to a system of quadratic equations of the form $b_i=\lvert\bm{a}_i^*\bm{x}\rvert^2$, $i=1,2,\ldots,m$, e.g., the well-known NP-hard phase retrieval problem. As opposed to recently proposed…
Massive MIMO systems are seen by many researchers as a paramount technology toward next generation networks. This technology consists of hundreds of antennas that are capable of sending and receiving simultaneously a huge amount of data.…
This paper considers signal detection in massive multiple-input multiple-output (MIMO) systems with general additive hardware impairments and one-bit quantization. First, we present the quantization-unaware and Bussgang decomposition-based…
Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…
The semidefinite programming (SDP) relaxation has proven to be extremely strong for many hard discrete optimization problems. This is in particular true for the quadratic assignment problem (QAP), arguably one of the hardest NP-hard…
Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…
In this work, based on the ideas of alternating direction method with multipliers (ADMM) and sequential quadratic programming (SQP), as well as Armijo line search technology, monotone splitting SQP algorithms for two-block nonconvex…
Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \sum_{i \ne j} a_{ij} x_i x_j. QP captures many known combinatorial optimization problems, and assuming the unique games conjecture,…
In this paper, we introduce HPR-QP, a dual Halpern Peaceman-Rachford (HPR) method designed for solving large-scale convex composite quadratic programming. One distinctive feature of HPR-QP is that, instead of working with the primal…
There is growing interest in solving computer vision problems such as mesh or point set alignment using Adiabatic Quantum Computing (AQC). Unfortunately, modern experimental AQC devices such as D-Wave only support Quadratic Unconstrained…
Multiple-input multiple-output (MIMO) technology applied with orthogonal frequency division multiplexing (OFDM) is considered as the ultimate solution to increase channel capacity without any additional spectral resources. At the receiver…
Physical design refers to mathematical optimization of a desired objective (e.g. strong light--matter interactions, or complete quantum state transfer) subject to the governing dynamical equations, such as Maxwell's or Schrodinger's…