Related papers: A Scalable Semidefinite Relaxation Approach to Gri…
We propose a new method for generating semidefinite relaxations of optimal power flow problems. The method is based on chordal conversion techniques: by dropping some equality constraints in the conversion, we obtain semidefinite…
For verifying the safety of neural networks (NNs), Fazlyab et al. (2019) introduced a semidefinite programming (SDP) approach called DeepSDP. This formulation can be viewed as the dual of the SDP relaxation for a problem formulated as a…
Many nonconvex problems in robotics can be relaxed into convex formulations via Semi-Definite Programming (SDP) that can be solved to global optimality. The practical quality of these solutions, however, critically depends on rounding them…
Stability and protection of the electrical power systems are always of primary concern. Stability can be affected mostly by increase in the load demand. Power grids are overloaded in peak hours so more power generation units are required to…
Many engineered systems, such as energy and transportation infrastructures, are networks governed by non-linear physical laws. A primary challenge for operators of these networks is to achieve optimal utilization while maintaining safety…
A semidefinite programming (SDP) relaxation globally solves many optimal power flow (OPF) problems. For other OPF problems where the SDP relaxation only provides a lower bound on the objective value rather than the globally optimal decision…
Power System Resource Planning is the recurrent process of studying and determining what facilities and procedures should be provided to satisfy and promote appropriate future demands for electricity. The electric power system as planned…
We propose three novel mathematical optimization formulations that solve the same two-type heterogeneous multiprocessor scheduling problem for a real-time taskset with hard constraints. Our formulations are based on a global scheduling…
Nonconvexities in markets with discrete decisions and nonlinear constraints make efficient pricing challenging, often necessitating subsidies. A prime example is the unit commitment (UC) problem in electricity markets, where costly…
In this paper, we develop a Topological Approximate Dynamic Programming (TADP) method for planningin stochastic systems modeled as Markov Decision Processesto maximize the probability of satisfying high-level systemspecifications expressed…
Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
The classic pump scheduling or Optimal Water Flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally…
This paper presents a scenario based robust optimization framework for short term energy scheduling in electricity intensive industrial plants, explicitly addressing uncertainty in planning decisions. The model is formulated as a two-stage…
This paper introduces OptimizedDP, a high-performance software library for several common grid-based dynamic programming (DP) algorithms used in control theory and robotics. Specifically, OptimizedDP provides functions to numerically solve…
We study Nonpreemptive Peak Demand Minimization (NPDM) problem, where we are given a set of jobs, specified by their processing times and energy requirements. The goal is to schedule all jobs within a fixed time period such that the peak…
Distribution networks are usually multiphase and radial. To facilitate power flow computation and optimization, two semidefinite programming (SDP) relaxations of the optimal power flow problem and a linear approximation of the power flow…
Semidefinite programming (SDP) provides a principled framework for convex relaxations of nonconvex geometric constraints in motion planning, yet existing solvers are too computationally expensive for real-time control, particularly on…
This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation method. We first introduce two SDP relaxation methods for solving polynomial optimization problems with finitely many…
The integration of more renewable energy sources into the power system is presenting system operators with various challenges. At the distribution system level, voltage magnitudes that violate operating limits near large photovoltaic…
The arrival of small-scale distributed energy generation in the future smart grid has led to the emergence of so-called prosumers, who can both consume as well as produce energy. By using local generation from renewable energy resources,…