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Price promotion optimization is a computationally challenging problem central to supermarket operations, requiring simultaneous pricing decisions across multiple products and periods. This paper introduces a novel formulation for…
This paper examines the performance trade-offs between an introduced linear flexibility market model for congestion management and a benchmark second-order cone programming (SOCP) formulation. The linear market model incorporates voltage…
Demand response (DR) has been demonstrated to be an effective method for reducing peak load and mitigating uncertainties on both the supply and demand sides of the electricity market. One critical question for DR research is how to…
In this study, we develop a theoretical model of strategic equilibrium bidding and price-setting behaviour by heterogeneous and boundedly rational electricity producers and a grid operator in a single electricity market under uncertain…
We consider semidefinite programming (SDP) for the binary stochastic block model with equal-sized communities. Prior work of Hajek, Wu, and Xu proposed an SDP (sym-SDP) for the symmetric case where the intra-community edge probabilities are…
Adversarial training is well-known to produce high-quality neural network models that are empirically robust against adversarial perturbations. Nevertheless, once a model has been adversarially trained, one often desires a certification…
In an electric power system, demand fluctuations may result in significant ancillary cost to suppliers. Furthermore, in the near future, deep penetration of volatile renewable electricity generation is expected to exacerbate the variability…
We investigate expected utility maximization problems from the terminal liquidation value in continuous time in markets with transaction costs and one fixed consistent price system, where a non-concave utility function is defined on the…
We have observed an interesting, yet unexplained, phenomenon: Semidefinite programming (SDP) based relaxations of maximum likelihood estimators (MLE) tend to be tight in recovery problems with noisy data, even when MLE cannot exactly…
We present a new generic approach to the condensed-matter ground-state problem which is complementary to variational techniques and works directly in the thermodynamic limit. Relaxing the ground-state problem, we obtain semidefinite…
Recently, there is growing interest and need for dynamic pricing algorithms, especially, in the field of online marketplaces by offering smart pricing options for big online stores. We present an approach to adjust prices based on the…
Wholesale market participation of storage with state-of-charge (SoC) dependent bids results in a non-convex cost in a multi-interval economic dispatch, which requires a mixed-integer linear program in the market clearing. We show that the…
This article presents a new method for computing guaranteed convex and concave relaxations of nonlinear stochastic optimal control problems with final-time expected-value cost functions. This method is motivated by similar methods for…
The current bottleneck of globally solving mixed-integer (non-convex) quadratically constrained problem (MIQCP) is still to construct strong but computationally cheap convex relaxations, especially when dense quadratic functions are…
In computer vision, many problems such as image segmentation, pixel labelling, and scene parsing can be formulated as binary quadratic programs (BQPs). For submodular problems, cuts based methods can be employed to efficiently solve…
We study a unified framework for optimization problems defined on dual-modular instances, where the input comprises a finite ground set $V$ and two set functions: a monotone supermodular reward function $\f$ and a strictly monotone…
This paper is concerned with optimal power flow (OPF), which is the problem of optimizing the transmission of electricity in power systems. Our main contributions are as follows: (i) we propose a novel parabolic relaxation, which transforms…
We propose a decentralized market model in which agents can negotiate bilateral contracts. This builds on a similar, but centralized, model of trading networks introduced by Hatfield et al. in 2013. Prior work has established that…
Boolean quadratic optimization problems occur in a number of applications. Their mixed integer-continuous nature is challenging, since it is inherently NP-hard. For this motivation, semidefinite programming relaxations (SDR's) are proposed…
Under the linear regression framework, we study the variable selection problem when the underlying model is assumed to have a small number of nonzero coefficients (i.e., the underlying linear model is sparse). Non-convex penalties in…