Related papers: Automating the formulation and resolution of conve…
This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…
A convex partition of a point set P in the plane is a planar partition of the convex hull of P with empty convex polygons or internal faces whose extreme points belong to P. In a convex partition, the union of the internal faces give 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,…
This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control,…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
We consider the problem of minimizing a finite sum of convex functions subject to the set of minimizers of a convex differentiable function. In order to solve the problem, an algorithm combining the incremental proximal gradient method with…
Minimax optimization has been central in addressing various applications in machine learning, game theory, and control theory. Prior literature has thus far mainly focused on studying such problems in the continuous domain, e.g.,…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
For those acquainted with CVX (aka disciplined convex programming) of M. Grant and S. Boyd, the motivation of this work is the desire to extend the scope of CVX beyond convex minimization -- to convex-concave saddle point problems and…
Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…
In this paper, we study a class of fractional semi-infinite polynomial programming (FSIPP) problems, in which the objective is a fraction of a convex polynomial and a concave polynomial, and the constraints consist of infinitely many convex…
Procrustes problems are matrix approximation problems searching for a~transformation of the given dataset to fit another dataset. They find applications in numerous areas, such as factor and multivariate analysis, computer vision,…
This paper introduces the FEDM (Finite Element Discharge Modelling) code, which was developed using the open-source computing platform FEniCS (https://fenicsproject.org). Building on FEniCS, the FEDM code utilises the finite element method…
Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…
In this paper, a convex optimization-based method is proposed for numerically solving dynamic programs in continuous state and action spaces. The key idea is to approximate the output of the Bellman operator at a particular state by the…
Domain-specific high-productivity environments are playing an increasingly important role in scientific computing due to the levels of abstraction and automation they provide. In this paper we introduce Devito, an open-source…
We consider the problem of inverse kinematics (IK), where one wants to find the parameters of a given kinematic skeleton that best explain a set of observed 3D joint locations. The kinematic skeleton has a tree structure, where each node is…
We present an efficient and robust numerical algorithm for solving the two-dimensional linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve…