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Electricity market operators worldwide use mixed-integer linear programming to solve the allocation problem in wholesale electricity markets. Prices are typically determined based on the duals of relaxed versions of this optimization…
The non-convex complementarity constraints present a fundamental computational challenge in energy constrained optimization problems. In this work, we present a new, linear, and robust battery optimization formulation that sidesteps the…
The system operator's scheduling problem in electricity markets, called unit commitment, is a non-convex mixed-integer program. The optimal value function is non-convex, preventing the application of traditional marginal pricing theory to…
Fuel cost contributes to a significant portion of operating cost in cargo transportation. Though classic routing models usually treat fuel cost as input data, fuel consumption heavily depends on the travel speed, which has led to the study…
In the literature, when optimizing the sizing and operation of a residential PV system in combination with a battery energy storage system, the efficiency of the battery and the converter is generally assumed constant, which corresponds to…
This paper instantiates a convex electric powertrain design optimization framework, bridging the gap between high-level powertrain sizing and low-level components design. We focus on the electric motor and transmission of electric vehicles,…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration…
Battery-hybrid power source architectures can reduce fuel consumption and emissions for ships with diverse operation profiles. However, conventional control strategies may fail to improve performance if the future operation profile is…
We examine a class of optimization problems involving the optimal operation of a single lossy energy storage system, where energy losses occur during charging and discharging. These inefficiencies typically lead to a nonconvex set of…
We combine the power flow model with the proportionally fair optimization criterion to study the control of congestion within a distribution electric grid network. The form of the mathematical optimization problem is a convex second order…
This paper proposes a convex non-linear cost saving model for optimal economic dispatch in a microgrid. The mod-el incorporates energy storage degradation cost and intermittent renewable generation. Cell degradation cost being a non-linear…
We consider fixed load power market with non-convexities originating from start-up and no-load costs of generators. The convex hull (minimal uplift) pricing method results in power prices minimizing the total uplift payments to generators,…
We consider a general power market with price-sensitive consumer bids and non-convexities originating from supply (start-up and no-load costs, nonzero minimum output limits of generating units, etc.) and demand. The convex hull…
We consider an important problem in the shipping industry known as the liner shipping fleet repositioning problem (LSFRP). We examine a public data set for this problem including many instances which have not previously been solved to…
We consider the convex quadratic optimization problem with indicator variables and arbitrary constraints on the indicators. We show that a convex hull description of the associated mixed-integer set in an extended space with a quadratic…
We address the problem of finding an optimal policy in a Markov decision process under a restricted policy class defined by the convex hull of a set of base policies. This problem is of great interest in applications in which a number of…
In this paper, we study the problem of optimizing the size and mix of a mixed fleet of electric and conventional vehicles owned by firms providing urban freight logistics services. Uncertain customer requests are considered at the strategic…
We present a novel complex number formulation along with tight convex relaxations for the aircraft conflict resolution problem. Our approach combines both speed and heading control and provides global optimality guarantees despite…
This paper investigates the scheduling problem of a fleet of electric vehicles, providing mobility as a service to a set of time-specified customers, where the operator needs to solve the routing and charging problem jointly for each EV.…