Related papers: Solving Conic Programs over Sparse Graphs using a …
The Optimal Power Flow (OPF) problem is central to the reliable and efficient operation of power systems, yet its non-convex nature poses significant challenges for finding globally optimal solutions. While convex relaxation techniques such…
Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization…
Optimal power flow (OPF) is a central problem in the operation of electric power systems. An OPF problem optimizes a specified objective function subject to constraints imposed by both the non-linear power flow equations and engineering…
Stochastic gradient method (SGM) has been popularly applied to solve optimization problems with objective that is stochastic or an average of many functions. Most existing works on SGMs assume that the underlying problem is unconstrained or…
Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce…
The security-constrained optimal power flow (SCOPF) is fundamental in power systems and connects the automatic primary response (APR) of synchronized generators with the short-term schedule. Every day, the SCOPF problem is repeatedly solved…
Stochastic gradient methods (SGMs) have been widely used for solving stochastic optimization problems. A majority of existing works assume no constraints or easy-to-project constraints. In this paper, we consider convex stochastic…
In this paper, we introduce a primal-dual algorithmic framework for solving Symmetric Cone Programs (SCPs), a versatile optimization model that unifies and extends Linear, Second-Order Cone (SOCP), and Semidefinite Programming (SDP). Our…
The DC Optimal Power Flow (DC-OPF) problem is fundamental to power system operations, requiring rapid solutions for real-time grid management. While traditional optimization solvers provide optimal solutions, their computational cost…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
We propose a new method for linear second-order cone programs. It is based on the sequential quadratic programming framework for nonlinear programming. In contrast to interior point methods, it can capitalize on the warm-start capabilities…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
The Linear Quadratic Gaussian (LQG) problem is a classic and widely studied model in optimal control, providing a fundamental framework for designing controllers for linear systems subject to process and observation noises. In recent years,…
Security-Constrained Optimal Power Flow (SCOPF) plays a crucial role in power grid stability but becomes increasingly complex as systems grow. This paper introduces PDL-SCOPF, a self-supervised end-to-end primal-dual learning framework for…
This paper proves that non-convex quadratically constrained quadratic programs can be solved in polynomial time when their underlying graph is acyclic, provided the constraints satisfy a certain technical condition. When this condition is…
Variational quantum circuits characterise the state of a quantum system through the use of parameters that are optimised using classical optimisation procedures that typically rely on gradient information. The circuit-execution complexity…
The optimal power flow (OPF) problem, which plays a central role in operating electrical networks is considered. The problem is nonconvex and is in fact NP hard. Therefore, designing efficient algorithms of practical relevance is crucial,…
An earlier work [18] proposes a method for solving the Lagrangian dual of a constrained binary quadratic programming problem via quantum adiabatic evolution using an outer approximation method. This should be an efficient prescription for…
We formulate the Alternating Current Optimal Power Flow Problem (ACOPF) as a Linear Constrained Quadratic Program (LCQP) with many negative eigenvalues ($r$) and linear constraints, making it NP-hard. We propose two algorithms, Feasible…