Abstract: A method operates a set of heating, ventilation and air-conditioning (HVAC) units by optimizing jointly operations of the set of HVAC units subject to constraints to determine times of switching each HVAC unit ON and OFF and by controlling each HVAC unit according to the corresponding times of switching. The operation of each HVAC unit is represented by a continuous function. The constraints include a complementarity constraint for each HVAC unit, such that the complementarity constraint for the HVAC unit defines a discontinuity of the operation of the HVAC unit at corresponding times of switching.

Abstract: Systems and Methods for controlling a movement of cars of an elevator system. A processor determines for each car an individual waiting time of each hall call. Determines for each pair of hall calls assigned for each car, a pairwise delay over the individual waiting time of each hall call in the pair caused by a joint assignment of the car to the pair of the hall calls. Approximate a cumulative waiting time of an assignment of the cars to the hall calls as a sum of individual waiting times for each hall call with the assigned car and a sum of all pairwise delays determined between all pairs of hall calls assigned to the same car. Determine the assignment of the cars using a greedy optimization algorithm that greedily assigns hall calls to the cars to minimize the approximated cumulative waiting time, and control the movement of the cars.

Abstract: Systems and Methods for controlling a movement of cars of an elevator system. A processor determines for each car an individual waiting time of each hall call. Determines for each pair of hall calls assigned for each car, a pairwise delay over the individual waiting time of each hall call in the pair caused by a joint assignment of the car to the pair of the hall calls. Approximate a cumulative waiting time of an assignment of the cars to the hall calls as a sum of individual waiting times for each hall call with the assigned car and a sum of all pairwise delays determined between all pairs of hall calls assigned to the same car. Determine the assignment of the cars using a greedy optimization algorithm that greedily assigns hall calls to the cars to minimize the approximated cumulative waiting time, and control the movement of the cars.

Abstract: A method solves a convex quadratic program (QP) for a convex set. Constrains of the QP include sets of linear equalities and linear inequalities. The solving uses an Alternating Direction Method of Multipliers (ADMM). Variables of the convex QP include a linear subspace constrained variable vector and a set constrained variable vector. The method solves the linear subspace constrained variable vector while keeping the set constrained variable vector fixed using an optimal step size and a Lagrangian multiplier, and solves the set of constrained variable vector while keeping linear subspace constrained variable vector fixed using the optimal step size and the Lagrangian multiplier. Then, the Lagrangian multiplier is updated. A feasible solution is outputted if a termination condition for the feasible solution is satisfied, and an infeasible solution is signaled if a termination condition for the satisfied for the infeasible solution is satisfied. Otherwise, the steps are repeated.

Abstract: A method for determining a pose of an object in a scene by determining a set of scene features from data acquired of the scene and matching the scene features to model features to generate weighted candidate poses when the scene feature matches one of the model features, wherein the weight of the candidate pose is proportional to the model weight. Then, the pose of the object is determined from the candidate poses based on the weights.

Abstract: A method determines a power flow of a power grid by optimizing an objective function representing an operation of the power grid using a spatial branch and bound (BB) framework for determining iteratively upper and lower bounds of the objective function. During the optimization, the lower bounds are determined using a semi-definite programming (SDP) relaxation of an optimal power flow (OPF) problem.

Abstract: A method operates a set of heating, ventilation and air-conditioning (HVAC) units by optimizing jointly operations of the set of HVAC units subject to constraints to determine times of switching each HVAC unit ON and OFF and by controlling each HVAC unit according to the corresponding times of switching. The operation of each HVAC unit is represented by a continuous function. The constraints include a complementarity constraint for each HVAC unit, such that the complementarity constraint for the HVAC unit defines a discontinuity of the operation of the HVAC unit at corresponding times of switching.

Abstract: Power flow in an electric power network is optimized during multiple time periods of operation of the electric power network by solving an optimization problem represented by an objective function by first initializing variables and constraints of a branch and bound (BB) tree, wherein nodes in the BB tree represent feasible regions of the optimization problem. Upper and lower bounds on the objective function are solved using the BB tree. A lowest upper bound and a lowest upper bound are updated. If difference between the lowest lower bound and the lowest upper bound is less than a threshold, the power flow is outputted based on the lowest lower bound and the lowest upper bound.

Abstract: A method solves a convex quadratic program (QP) for a convex set. Constrains of the QP include sets of linear equalities and linear inequalities. The solving uses an Alternating Direction Method of Multipliers (ADMM). Variables of the convex QP include a linear subspace constrained variable vector and a set constrained variable vector. The method solves the linear subspace constrained variable vector while keeping the set constrained variable vector fixed using an optimal step size and a Lagrangian multiplier, and solves the set of constrained variable vector while keeping linear subspace constrained variable vector fixed using the optimal step size and the Lagrangian multiplier. Then, the Lagrangian multiplier is updated. A feasible solution is outputted if a termination condition for the feasible solution is satisfied, and an infeasible solution is signaled if a termination condition for the satisfied for the infeasible solution is satisfied. Otherwise, the steps are repeated.

Abstract: A method determines a power flow of a power grid by optimizing an objective function representing an operation of the power grid using a spatial branch and bound (BB) framework for determining iteratively upper and lower bounds of the objective function. During the optimization, the lower bounds are determined using a semi-definite programming (SDP) relaxation of an optimal power flow (OPF) problem.

Abstract: A system and method optimizes energy consumption in a railway system including a set of trains, a set of energy storage devices, and a set of substations connected to a grid by first optimizing control parameters controlling at least part of the energy consumption of the railway system to produce optimized control parameters. The optimized control parameters minimize, over multiple time steps, a combination of total power provided by the grid to satisfy a power demand of the railway system, a state-of-charge of each energy storage device, power supplied to charge the energy storage device and power supplied by the energy storage device. The optimizing is subject to constraints on operations of the railway system over multiple time steps. The constraints include a complementarity constraint. A command is generated to control the energy consumption of the railway system based on the optimized control parameters.

Abstract: A method for determining a pose of an object in a scene by determining a set of scene features from data acquired of the scene and matching the scene features to model features to generate weighted candiate poses when the scene feature matches one of the model features, wherein the weight of the candidate pose is proportional to the model weight. Then, the pose of the object is determined from the candidate poses based on the weights.

Abstract: A heating, ventilation and air-conditioning (HVAC) system for a building is optimized while maximizing a comfort of occupants and minimizing energy consumption. The building is modeled as a network of nodes and edges, wherein the nodes represent rooms, and the edges represent walls. Dynamics of temperatures and humidity in the rooms and the temperature of the walls and the building are modeled using differential equations and the network. The comfort of the occupants is modeled by a predicted mean vote (PMV). The minimizing is formulated as an optimal control problem, which is discretized using an integration technique to obtain a finite dimensional optimization problem. Then, the finite dimensional optimization problem is solved using sparse linear algebra until convergence.

Abstract: A method optimizes energy consumption in a railway system including a set of trains and a set of substations connected to a grid. The method optimizes control parameters controlling at least part of the energy consumption of the railway system to produce optimized control parameters minimizing a total power provided by the grid to satisfy a power demand of the railway system. The optimizing is subject to constraints on operations of the railway system, which include as complementarity constraint. Next, the method generates a command to control the energy consumption of the railway system based on the optimized control parameters.

Abstract: A system and method optimizes energy consumption in a railway system including a set of trains, a set of energy storage devices, and a set of substations connected to a grid by first optimizing control parameters controlling at least part of the energy consumption of the railway system to produce optimized control parameters. The optimized control parameters minimize, over multiple time steps, a combination of total power provided by the grid to satisfy a power demand of the railway system, a state-of-charge of each energy storage device, power supplied to charge the energy storage device and power supplied by the energy storage device. The optimizing is subject to constraints on operations of the railway system over multiple time steps. The constraints include a complementarity constraint. A command is generated to control the energy consumption of the railway system based on the optimized control parameters.

Abstract: A method optimizes energy consumption in a railway system including a set of trains and a set of substations connected to a grid. The method optimizes control parameters controlling at least part of the energy consumption of the railway system to produce optimized control parameters minimizing a total power provided by the grid to satisfy a power demand of the railway system. The optimizing is subject to constraints on operations of the railway system, which include as complementarily constraint. Next, the method generates a command to control the energy consumption of the railway system based on the optimized control parameters.

Abstract: Power flow in an electric power network is optimized by first decomposing an optimization problem into a set of disjoint parameterized optimization problems. The disjoint optimization problems are independent of each other, and the decomposition is based on dualized coupled constraints having corresponding multipliers. Each optimization problem is solved independently to obtain a corresponding solution, and a sensitivity of each solution to changes in the parameter. The parameters are updated using the corresponding solutions and the sensitivities, and iterated until reaching a convergence.

Abstract: A method for determining a suitable configuration for an elevator system for a building that includes acquiring building related information and passenger use information. Elevator system performance requirements based on elevator system passenger numbers are selected based on this information followed by selecting a set of elevator system characteristic variables that are desired to be at optimal values which are processed along with the information and performance requirements to provide an optimal solution.