We present a novel semi-definite programming method which allows us to design custom proximal splitting algorithms for solving convex composite minimization problems. These algorithms can be tailored to the compute architecture and problem in a way that minimizes the expected time required to converge. We present convergence rates for these algorithms derived using the PEP framework, which also allows us to find the optimal step size for the algorithm.

We present results of an ARPA-E funded project under the PERFORM - Performance-based Energy Resource Feedback, Optimization, and Risk Management - program, which develops innovative management systems that represent the relative delivery risk of each asset, like wind farms, and balance the collective risk of all assets across the grid. We propose a New Risk Assessment and Management Paradigm designed to overhaul Electricity Markets by efficiently addressing uncertainty in the forthcoming massive renewable generation and electrification of fossil fuel reliant energy uses. We present methodologies constituting a risk-driven paradigm to achieve higher adoption of stochastic resources and a more efficient and reliable system operation, and we provide proof of concept on the Southwest Power Pool territory.

Renewable electricity systems underpin global decarbonization efforts. For computational tractability, capacity expansion models often employ simplifications of temporal or network details. Yet the value of new resource investments, such as storage or transmission, are affected by both temporal and spatial coupling. Improving accuracy motivates algorithmic improvements. Bundle method approaches are examined to solve nodal-resolution capacity expansion models with reasonable temporal resolution. Various practical implementation improvements are considered. Case studies are conducted on realistic large-scale US networks.