相关论文: Certifying Global Optimality of AC-OPF Solutions v…

In this paper, we consider polynomial optimization with correlative sparsity. We construct correlatively sparse Lagrange multiplier expressions (CS-LMEs) and propose CS-LME reformulations for polynomial optimization problems using the…

The existence of multiple solutions to AC optimal power flow (ACOPF) problems has been noted for decades. Existing solvers are generally successful in finding local solutions, which are stationary points but may not be globally optimal. In…

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle (SFO). We…

The energy transition is driving the integration of large shares of intermittent power sources in the electric power grid. Therefore, addressing the AC optimal power flow (AC-OPF) effectively becomes increasingly essential. The AC-OPF,…

A Transient Stability-Constrained Optimal Power Flow (TSC-OPF) problem is proposed that enforces frequency stability constraints using Neural Network (NN) surrogate models. NNs are trained using a novel model-driven active sampling…

We address the problem of symmetry reduction of optimal control problems under the action of a finite group from a measure relaxation viewpoint. We propose a method based on the moment-SOS aka Lasserre hierarchy which allows one to…

Optimal transport (OT) is a powerful tool in mathematics and data science but faces severe computational and statistical challenges in high dimensions. We propose convex relaxation approaches based on marginal and cluster moment relaxations…

This is a second part of the research on AC optimal power flow being used in the lower level of the bilevel strategic bidding or investment models. As an example of a suitable upper-level problem, we observe a strategic bidding of energy…

The problem of high-dimensional path-dependent optimal stopping (OS) is important to multiple academic communities and applications. Modern OS tasks often have a large number of decision epochs, and complicated non-Markovian dynamics,…

We show that contact-rich motion planning is also sparsity-rich when viewed as polynomial optimization (POP). We can exploit not only the correlative and term sparsity patterns that are general to all POPs, but also specialized sparsity…

The thesis focuses on developing a data-driven algorithm, based on machine learning, to solve the stochastic alternating current (AC) chance-constrained (CC) Optimal Power Flow (OPF) problem. Although the AC CC-OPF problem has been…

Distributed Constraint Satisfaction (DCSP) has long been considered an important problem in multi-agent systems research. This is because many real-world problems can be represented as constraint satisfaction and these problems often…

This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and…

This paper presents exact Semi-Definite Program (SDP) reformulations for infinite-dimensional moment optimization problems involving a new class of piecewise Sum-of-Squares (SOS)-convex functions and projected spectrahedral support sets.…

We study the classical coalition structure generation (CSG) problem and compare the anytime behavior of three algorithmic paradigms: dynamic programming (DP), MILP branch-and-bound, and sparse relaxations based on greedy or $l_1$-type…

We propose a novel global solution algorithm for the network-constrained unit commitment problem incorporating a nonlinear alternating current model of the transmission network, which is a nonconvex mixed-integer nonlinear programming…

We analyze a zeroth-order particle algorithm for the global optimization of a non-convex function, focusing on a variant of Consensus-Based Optimization (CBO) with small but fixed noise intensity. Unlike most previous studies restricted to…

We study the Sum of Squares (SoS) Hierarchy with a view towards combinatorial optimization. We survey the use of the SoS hierarchy to obtain approximation algorithms on graphs using their spectral properties. We present a simplified proof…

In this work, we focus on the Partial Constraint Satisfaction Problem (PCSP) over control-flow graphs (CFGs) of programs. PCSP serves as a generalization of the well-known Constraint Satisfaction Problem (CSP). In the CSP framework, we…

We develop a fast and reliable method for solving large-scale optimal transport (OT) problems at an unprecedented combination of speed and accuracy. Built on the celebrated Douglas-Rachford splitting technique, our method tackles the…