Related papers: Deflation Techniques for Stellarator Equilibrium a…
Deflation techniques are typically used to shift isolated clusters of small eigenvalues in order to obtain a tighter distribution and a smaller condition number. Such changes induce a positive effect in the convergence behavior of Krylov…
Variational inequalities can in general support distinct solutions. In this paper we study an algorithm for computing distinct solutions of a variational inequality, without varying the initial guess supplied to the solver. The central idea…
A new approach to combinatorial optimization based on systematic move-class deflation is proposed. The algorithm combines heuristics of genetic algorithms and simulated annealing, and is mainly entropy-driven. It is tested on two problems…
A new perturbation and continuation method is presented for computing and analyzing stellarator equilibria. The method is formally derived from a series expansion about the equilibrium condition $F \equiv J \times B - \nabla p = 0$, and an…
Stellarator optimization often takes a two-stage approach, where in the first stage the boundary is varied in order to optimize for some physics metrics, while in the second stage the boundary is kept fixed and coils are sought to generate…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
Combined plasma-coil optimization approaches for designing stellarators are discussed and a new method for calculating free-boundary equilibria is proposed. Four distinct categories of stellarator optimization, two of which are novel…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…
In stellarators, achieving effective divertor configurations is challenging due to the three-dimensional nature of the magnetic fields, which often leads to chaotic field lines and fuzzy separatrices. This work presents a novel approach to…
Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…
This paper studies decentralized convex-concave minimax optimization problems of the form $\min_x\max_y f(x,y) \triangleq\frac{1}{m}\sum_{i=1}^m f_i(x,y)$, where $m$ is the number of agents and each local function can be written as…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…
The continuation method is a popular approach in non-convex optimization and computer vision. The main idea is to start from a simple function that can be minimized efficiently, and gradually transform it to the more complicated original…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
We propose a new decomposition framework for continuous nonlinear constrained two-stage optimization, where both first- and second-stage problems can be nonconvex. A smoothing technique based on an interior-point formulation renders the…
This paper studies consensus-based decentralized stochastic optimization for minimizing possibly non-convex expected objectives with convex non-smooth regularizers and nonlinear functional inequality constraints. We reformulate the…
There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…