Related papers: The QC Relaxation: Theoretical and Computational R…
We consider linear and semidefinite programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT relaxation), and the Shor relaxation combined with the RLT relaxation (SDP-RLT relaxation).…
As the modern transmission control and relay technologies evolve, transmission line switching has become an important option in power system operators' toolkits to reduce operational cost and improve system reliability. Most recent research…
The Alternating Current Optimal Power Flow (ACOPF) problem remains one of the most fundamental yet computationally challenging tasks in power systems operation and planning due to its nonconvex, nonlinear, and multimodal nature. This paper…
Combined heat and power dispatch promotes interactions and synergies between electric power systems and district heating systems. However, nonlinear and nonconvex heating flow imposes significant challenges on finding qualified solutions…
We study the maximization of sums of heterogeneous quadratic forms over the Stiefel manifold, a nonconvex problem that arises in several modern signal processing and machine learning applications such as heteroscedastic probabilistic…
We consider the exact solution of problem $(QP)$ that consists in minimizing a quadratic function subject to quadratic constraints. Starting from the classical convex relaxation that uses the McCormick's envelopes, we introduce 12…
DC Optimal Power Flow (DC-OPF) problems optimize the generators' active power setpoints while satisfying constraints based on the DC power flow linearization. The computational tractability advantages of DC-OPF problems come at the expense…
The Optimal Power Flow (OPF) problem is integral to the functioning of power systems, aiming to optimize generation dispatch while adhering to technical and operational constraints. These constraints are far from straightforward; they…
We consider the strictly correlated electron (SCE) limit of the fermionic quantum many-body problem in the second-quantized formalism. This limit gives rise to a multi-marginal optimal transport (MMOT) problem. Here the marginal state space…
High Voltage Direct Current (HVDC) systems interconnect AC grids to increase reliability, connect offshore wind generation, and enable coupling of electricity markets. Considering the growing uncertainty in power infeed and the complexity…
This paper investigates a combinatorial optimization problem motived from a secure power network design application in [D\'{a}n and Sandberg 2010]. Two equivalent graph optimization formulations are derived. One of the formulations is a…
Alternating current optimal power flow (AC OPF) is one of the most fundamental optimization problems in electrical power systems. It can be formulated as a semidefinite program (SDP) with rank constraints. Solving AC OPF, that is, obtaining…
In this paper, we introduce a new class of nonsmooth convex functions called SOS-convex semialgebraic functions extending the recently proposed notion of SOS-convex polynomials. This class of nonsmooth convex functions covers many common…
This paper develops new semidefinite programming (SDP) relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs (MBQCQP) and analyzes their approximation performance. The first class of problem…
The economic dispatch problem is considered for unbalanced three-phase power distribution networks entailing both non-deferrable and elastic loads, and distributed generation (DG) units. The objective is to minimize the costs of power drawn…
In the first part of this work [32], we introduce a convex parabolic relaxation for quadratically-constrained quadratic programs, along with a sequential penalized parabolic relaxation algorithm to recover near-optimal feasible solutions.…
Multi-terminal high voltage direct current (MTHVDC) technology is a promising technology for the offshore wind farm integration, which requires the new control and operation scheme. Therefore, the optimal power flow problem for this system…
Sparse principal component analysis (PCA) involves nonconvex optimization for which the global solution is hard to obtain. To address this issue, one popular approach is convex relaxation. However, such an approach may produce suboptimal…
We develop tractable convex relaxations for rank-constrained quadratic optimization problems over $n \times m$ matrices, a setting for which tractable relaxations are typically only available when the objective or constraints admit spectral…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…