Related papers: Pricing Discrete and Nonlinear Markets With Semide…
We investigate exact semidefinite programming (SDP) relaxations for the problem of minimizing a nonconvex quadratic objective function over a feasible region defined by both finitely and infinitely many nonconvex quadratic inequality…
We present new formulations of the stochastic electricity market clearing problem based on the principles of stochastic programming. Previous analyses have established that the canonical stochastic programming model effectively captures the…
We study semidefinite programming (SDP) relaxations for the NP-hard problem of globally optimizing a quadratic function over the Stiefel manifold. We introduce a strengthened relaxation based on two recent ideas in the literature: (i) a…
This paper considers state-of-the-art convex relaxations for the AC power flow equations and introduces new valid cuts based on convex envelopes and lifted nonlinear constraints. These valid linear inequalities strengthen existing…
We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art…
Efficiently accommodating uncertain renewable resources in wholesale electricity markets is among the foremost priorities of market regulators in the US, UK and EU nations. However, existing deterministic market designs fail to internalize…
Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…
We present a novel, practical, and provable approach for solving diagonally constrained semi-definite programming (SDP) problems at scale using accelerated non-convex programming. Our algorithm non-trivially combines acceleration motions…
We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a num\'eraire-based semi-static utility maximization problem with an exponential utility preference. The randomization…
Market equilibrium is a solution concept with many applications such as digital ad markets, fair division, and resource sharing. For many classes of utility functions, equilibria can be captured by convex programs. We develop simple…
Recently, there has been significant interest in convex relaxations of the optimal power flow (OPF) problem. A semidefinite programming (SDP) relaxation globally solves many OPF problems. However, there exist practical problems for which…
An optimization problem considering AC power flow constraints and integer decision variables can usually be posed as a mixed-integer quadratically constrained quadratic program (MIQCQP) problem. In this paper, first, a set of valid linear…
Distribution locational marginal prices (DLMPs) facilitate the efficient operation of low-voltage electric power distribution systems. We propose an approach to internalize the stochasticity of renewable distributed energy resources (DERs)…
Visualizing graphs using virtual physical models is probably the most heavily used technique for drawing graphs in practice. There are many algorithms that are efficient and produce high-quality layouts. If one requires that the layout also…
We consider the problem of co-optimized energy-reserve market clearing with state-of-charge (SoC) dependent bids from battery storage participants. While SoC-dependent bids capture storage's degradation and opportunity costs, such bids…
This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…
This paper proposes a market mechanism for multi-interval electricity markets with generator and storage participants. Drawing ideas from supply function bidding, we introduce a novel bid structure for storage participation that allows…
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…
In the presence of non-convexities, the power market may not have an equilibrium price for power that provides economic stability of the centralized dispatch outcome. In this case, to achieve an economically stable outcome, the uplift…
We study binary optimization problems of the form \( \min_{x\in\{-1,1\}^n} f(Ax-b) \) with possibly nonsmooth loss \(f\). Following the lifted rank-one semidefinite programming (SDP) approach\cite{qian2023matrix}, we develop a…