Related papers: Improved Sufficient Conditions for Exact Convex Re…
Storage-concerned economic dispatch (ED) problems with complementarity constraints are strongly non-convex and hard to solve because traditional Karush-Kuhn-Tucker (KKT) conditions do not hold in this condition. In our recent paper, we…
Storage-concerned Optimal Power Flow (OPF) with complementarity constraints is highly non-convex and intractable. In this paper, we propose two generalized sufficient conditions which guarantee no simultaneous charging and discharging (SCD)…
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…
When modeling energy storage systems, an essential question is how to account for the physical infeasibility of simultaneous charge and discharge. The use of complementarity constraints or of binary variables is common, but these…
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…
In this letter, we model the day-ahead price-based demand response of a residential household with battery energy storage and other controllable loads, as a convex optimization problem. Further using duality theory and Karush-Kuhn-Tucker…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…
The economic dispatch problem is considered for unbalanced three-phase power distribution networks entailing both non-deferrable and elastic loads, and distributed generation (DG) units. The objective is to minimize the costs of power drawn…
We establish a geometric condition guaranteeing exact copositive relaxation for the nonconvex quadratic optimization problem under two quadratic and several linear constraints, and present sufficient conditions for global optimality in…
Discrete Lossless Convexification (DLCvx) formulates a convex relaxation for a specific class of discrete-time non-convex optimal control problems. It establishes sufficient conditions under which the solution of the relaxed problem…
Convex relaxations of the optimal power flow (OPF) problem provide an efficient alternative to solving the intractable alternating current (AC) optimal power flow. The conic subset of OPF convex relaxations, in particular, greatly…
Economic dispatch problem for a networked power system has been considered. The objective is to minimize the total generation cost while meeting the overall supply-demand balance and generation capacity. In particular, a more practical…
To solve the AC optimal power flow problem, it is proposed in [1,2] that a convex conic approximation to branch flow model (BFM) can be obtained if we first eliminate phase angles of voltages and currents and then relax a set of equality…
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…
A convex relaxation of a quadratically constrained quadratic program (QCQP) is called exact if it has a rank-$1$ optimal solution that corresponds to an optimal solution of the QCQP. Given a QCQP whose convex relaxation is exact, this paper…
This paper presents a convex optimization framework for eco-driving and vehicle energy management problems. We will first show that several types of eco-driving and vehicle energy management problems can be modelled using the same notions…
This work addresses the occupation measure relaxation of calculus of variations problems, which is an infinite-dimensional linear programming relaxation amenable to numerical approximation by a hierarchy of semidefinite optimization…
We study distributed convex optimization with two ubiquitous forms of coupling: consensus constraints and global affine equalities. We first design a linearized method of multipliers for the consensus optimization problem. Without…
We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. These are obtained as the lower semicontinuous and convex…
This paper addresses the well posedness of a dynamical model of perfect plasticity with mixed boundary conditions for general closed and convex elasticity sets. The proof relies on an asymptotic analysis of the solution of a perfect…