Dual descent ALM and ADMM

\(\) Classical primal-dual algorithms attempt to solve $\max_{\mu}\min_{x} \mathcal{L}(x,\mu)$ by alternatively minimizing over the primal variable $x$ through primal descent and maximizing the dual variable $\mu$ through dual ascent. However, when $\mathcal{L}(x,\mu)$ is highly nonconvex with complex constraints in $x$, the minimization over $x$ may not achieve global optimality, and hence the dual ascent step … Read more

Algorithms for Difference-of-Convex (DC) Programs Based on Difference-of-Moreau-Envelopes Smoothing

In this paper we consider minimization of a difference-of-convex (DC) function with and without linear constraints. We first study a smooth approximation of a generic DC function, termed difference-of-Moreau-envelopes (DME) smoothing, where both components of the DC function are replaced by their respective Moreau envelopes. The resulting smooth approximation is shown to be Lipschitz differentiable, … Read more

On Distributionally Robust Multistage Convex Optimization: New Algorithms and Complexity Analysis

This paper presents a novel algorithmic study and complexity analysis of distributionally robust multistage convex optimization (DR-MCO). We propose a new class of algorithms for solving DR-MCO, namely a sequential dual dynamic programming (Seq-DDP) algorithm and its nonsequential version (NDDP). The new algorithms generalize and strengthen existing DDP-type algorithms by introducing the technique of regularization … Read more

A Two-level ADMM Algorithm for AC OPF with Convergence Guarantees

This paper proposes a two-level distributed algorithmic framework for solving the AC optimal power flow (OPF) problem with convergence guarantees. The presence of highly nonconvex constraints in OPF poses significant challenges to distributed algorithms based on the alternating direction method of multipliers (ADMM). In particular, convergence is not provably guaranteed for nonconvex network optimization problems … Read more

Stochastic Dual Dynamic Programming for Multistage Stochastic Mixed-Integer Nonlinear Optimization

In this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stochastic convex optimization with \emph{non-Lipschitz-continuous} value functions and multistage stochastic mixed-integer linear optimization. We develop stochastic dual dynamic programming (SDDP) type algorithms with nested decomposition, deterministic sampling, and stochastic sampling. The key ingredient … Read more

A two-level distributed algorithm for nonconvex constrained optimization

This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are nonlinear power flow equations, or an abstract one that represents constraint couplings between decision variables of different agents. Despite the … Read more

Towards Resilient Operation of Multi-Microgrids: An MISOCP-Based Frequency-Constrained Approach

High penetration of distributed energy resources (DERs) is transforming the paradigm in power system operation. The ability to provide electricity to customers while the main grid is disrupted has introduced the concept of microgrids with many challenges and opportunities. Emergency control of dangerous transients caused by the transition between the grid-connected and island modes in … Read more

Leveraging Predictive Analytics to Control and Coordinate Operations, Asset Loading and Maintenance

This paper aims to advance decision-making in power systems by proposing an integrated framework that combines sensor data analytics and optimization. Our modeling framework consists of two components: (1) a predictive analytics methodology that uses real-time sensor data to predict future degradation and remaining lifetime of generators as a function of the loading conditions, and … Read more

The Adaptive Robust Multi-Period Alternating Current Optimal Power Flow Problem

This paper jointly addresses two major challenges in power system operations: i) dealing with non-convexity in the power flow equations, and ii) systematically capturing uncertainty in renewable power availability and in active and reactive power consumption at load buses. To overcome these challenges, this paper proposes a two-stage adaptive robust optimization model for the multi-period … Read more

A New Voltage Stability-Constrained Optimal Power Flow Model: Sufficient Condition, SOCP Representation, and Relaxation

A simple characterization of the solvability of power flow equations is of great importance in the monitoring, control, and protection of power systems. In this paper, we introduce a sufficient condition for power flow Jacobian nonsingularity. We show that this condition is second-order conic representable when load powers are fixed. Through the incorporation of the … Read more