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In 2020, Yamakawa and Okuno proposed a stabilized sequential quadratic semidefinite programming (SQSDP) method for solving, in particular, degenerate nonlinear semidefinite optimization problems. The algorithm is shown to converge globally…
Large scale, non-convex optimization problems arising in many complex networks such as the power system call for efficient and scalable distributed optimization algorithms. Existing distributed methods are usually iterative and require…
Although stochastic gradient descent (SGD) method and its variants (e.g., stochastic momentum methods, AdaGrad) are the choice of algorithms for solving non-convex problems (especially deep learning), there still remain big gaps between the…
Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they…
It has been shown in \cite{Lan13-1} that the accelerated prox-level (APL) method and its variant, the uniform smoothing level (USL) method, have optimal iteration complexity for solving black-box and structured convex programming problems…
This paper applies Benders decomposition to two-stage stochastic problems for energy planning under climate uncertainty, a key problem for the design of renewable energy systems. To improve performance, we adapt various refinements for…
Optimal power flow (OPF) problem is a class of large-scale and non-convex optimization problem. Various algorithms are proposed to solve the challenging OPF problem. Recent studies show that semidefinite programming (SDP) can either provide…
This paper deals with the impact of linear approximations for the unknown nonconvex confidence region of chance-constrained AC optimal power flow problems. Such approximations are required for the formulation of tractable chance…
We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is…
Formulating the alternating current optimal power flow (ACOPF) as a polynomial optimization problem makes it possible to solve large instances in practice and to guarantee asymptotic convergence in theory.
In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
In order to coordinate the economy and voltage quality of a meshed AC/VSC-MTDC system, a new corrective security-constrained multi-objective optimal power flow (SC-MOPF) method is presented in this paper. A parallel SC-MOPF model with N-1…
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 satisfy first and second order optimality conditions, but…
Consider a polynomial optimisation problem, whose instances vary continuously over time. We propose to use a coordinate-descent algorithm for solving such time-varying optimisation problems. In particular, we focus on relaxations of…
Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential applications in risk-averse machine learning, semisupervised learning, and robust optimization…
The DC optimal power flow (DCOPF) problem is a fundamental problem in power systems operations and planning. With high penetration of uncertain renewable resources in power systems, DCOPF needs to be solved repeatedly for a large amount of…
In this paper, we propose an inertial alternating direction method of multipliers for solving a class of non-convex multi-block optimization problems with \emph{nonlinear coupling constraints}. Distinctive features of our proposed method,…
This paper provides an enhanced modeling of the contingency response that collectively reflects high-fidelity physical and operational characteristics of power grids. Integrating active and reactive power contingency responses into the…
We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…
We propose a quantum-assisted framework for solving constrained finite-horizon nonlinear optimal control problems using a barrier Sequential Quadratic Programming (SQP) approach. Within this framework, a quantum subroutine is incorporated…