Related papers: Improving Optimal Power Flow Relaxations Using 3-C…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
The penetration of distributed energy resources (DERs) is increasing dramatically. Due to the uncertainty of DERs, the operation of the distribution system is facing higher risks and challenges. To overcome such challenges, a two-stage…
In this workshop, we present a compact but rigorous introduction to second-order optimality conditions for mathematical programs with equilibrium constraints (MPECs). We start from the classical nonlinear programming template, then explain…
We consider the minimization of a continuous function over the intersection of a regular cone with an affine set via a new class of adaptive first- and second-order optimization methods, building on the Hessian-barrier techniques introduced…
This paper is concerned with second-order optimality conditions for the mathematical program with semidefinite cone complementarity constraints (SDCMPCC).To achieve this goal, we first provide an exact characterization on the second-order…
We consider T-optimal experiment design problems for discriminating multi-factor polynomial regression models where the design space is defined by polynomial inequalities and the regression parameters are constrained to given convex sets.…
Converging hierarchies of finite-dimensional semi-definite relaxations have been proposed for state-constrained optimal control problems featuring oscillation phe-nomena, by relaxing controls as Young measures. These semi-definite…
In recent years, there has been a huge trend to penetrate renewable energy sources into energy networks. However, these sources introduce uncertain power generation depending on environmental conditions. Therefore, finding 'optimal' and…
Modern mesh generation pipelines whether learning-based or classical often produce outputs requiring post-processing to achieve production-quality geometry. This work introduces MeshCone, a convex optimization framework for guided mesh…
In this paper, we consider the problem of optimally coordinating the response of a group of distributed energy resources (DERs) in distribution systems by solving the so-called optimal power flow (OPF) problem. The OPF problem is concerned…
Various control schemes rely on a solution of a convex optimization problem involving a particular robust quadratic constraint, which can be reformulated as a linear matrix inequality using the well-known $\mathcal{S}$-lemma. However, the…
In this paper, we analyze optimal control problems governed by semilinear parabolic equations. Box constraints for the controls are imposed and the cost functional involves the state and possibly a sparsity-promoting term, but not a…
Unbalanced optimal power flow refers to a class of optimization problems subject to the steady state physics of three-phase power grids with nonnegligible phase unbalance. Significant progress on this problem has been made on the…
In this paper we consider the problem of distributed nonlinear optimisation of a separable convex cost function over a graph subject to cone constraints. We show how to generalise, using convex analysis, monotone operator theory and…
In this note, we present an elementary proof for a well-known second-order sufficient optimality condition in nonlinear semidefinite optimization which does not rely on the enhanced theory of second-order tangents. Our approach builds on an…
Linearized models of power systems are often desirable to formulate tractable control and optimization problems that still reflect real-world physics adequately under various operating conditions. In this paper, we propose an approach that…
We consider the problem of optimal input design for estimating uncertain parameters in a discrete-time linear state space model, subject to simultaneous amplitude and l1/l2-norm constraints on the admissible inputs. We formulate this…
Optimal power flow (OPF) is a fundamental tool for analyzing the characteristics of bipolar DC distribution network (DCDN). However, existing OPF models face challenges in reflecting the power distribution and exchange of bipolar DCDN…
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…
Load side participation can provide support to the power network by appropriately adapting the demand when required. In addition, it enables an economically improved power allocation. In this study, we consider the problem of providing an…