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Stellarator optimization is a multi-objective, non-convex problem characterized by a complex objective landscape containing many local minima. The solution resulting from a single optimization is highly sensitive to factors such as the…
Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex…
Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promote convergence to more optimal solutions;…
Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
Bayesian optimization is a popular and versatile approach that is well suited to solve challenging optimization problems. Their popularity comes from their effective minimization of expensive function evaluations, their capability to…
This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
High dimensional and/or nonconvex optimization remains a challenging and important problem across a wide range of fields, such as machine learning, data assimilation, and partial differential equation (PDE) constrained optimization. Here we…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
Recent work on Bayesian optimization has shown its effectiveness in global optimization of difficult black-box objective functions. Many real-world optimization problems of interest also have constraints which are unknown a priori. In this…
Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
In this paper, we study the decentralized optimization problem of minimizing a finite sum of continuously differentiable and possibly nonconvex functions over a fixed-connected undirected network. We propose a unified decentralized…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
Time-varying non-convex continuous-valued non-linear constrained optimization is a fundamental problem. We study conditions wherein a momentum-like regularising term allow for the tracking of local optima by considering an ordinary…
This paper defines a convertible nonconvex function(CN function for short) and a weak (strong) uniform (decomposable, exact) CN function, proves the optimization conditions for their global solutions and proposes algorithms for solving the…
The main challenge of nonconvex optimization is to find a global optimum, or at least to avoid ``bad'' local minima and meaningless stationary points. We study here the extent to which algorithms, as opposed to optimization models and…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a…