Related papers: Quantifying Non-linearity in Topology Optimization…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
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…
In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
We study the problem of Trajectory Optimization (TO) for a general class of stiff and constrained dynamic systems. We establish a set of mild assumptions, under which we show that TO converges numerically stably to a locally optimal and…
Topology optimization has matured to become a powerful engineering design tool that is capable of designing extraordinary structures and materials taking into account various physical phenomena. Despite the method's great advancements in…
We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…
Stochastic Optimal Control (SOC) problems arise in systems influenced by uncertainty, such as autonomous robots or financial models. Traditional methods like dynamic programming are often intractable for high-dimensional, nonlinear systems…
In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…
Dense image matching is a fundamental low-level problem in Computer Vision, which has received tremendous attention from both discrete and continuous optimization communities. The goal of this paper is to combine the advantages of discrete…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
Topology optimization (TO) has experienced a dramatic development over the last decades aided by the arising of metamaterials and additive manufacturing (AM) techniques, and it is intended to achieve the current and future challenges. In…
Optimization problems with both control variables and environmental variables arise in many fields. This paper introduces a framework of personalized optimization to han- dle such problems. Unlike traditional robust optimization,…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
While approaches to model the progression of fracture have received significant attention, methods to find the solution to the associated nonlinear equations have not. In general, nonlinear solution methods and optimization methods have a…
We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…
We use sensitivity analysis to design bounding-focused discretization (cutting-surface) methods for the global optimization of nonconvex semi-infinite programs (SIPs). We begin by formulating the optimal bounding-focused discretization of…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…
Graph vertex ordering is widely employed in spatial data analysis, especially in urban analytics, where street graphs serve as spatial discretization for modeling and simulation. It is also crucial for visualization, as many methods require…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…