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We present a level-set based topology optimization algorithm for design optimization problems involving an arbitrary number of different materials, where the evolution of a design is solely guided by topological derivatives. Our method can…
A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory…
The alternating direction method of multipliers (ADMM) has been widely adopted in low-rank approximation and low-order model identification tasks; however, the performance of nonconvex ADMM is highly reliant on the choice of penalty…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
We propose a novel semi-direct approach for monocular simultaneous localization and mapping (SLAM) that combines the complementary strengths of direct and feature-based methods. The proposed pipeline loosely couples direct odometry and…
Discrete optimization is a central problem in mathematical optimization with a broad range of applications, among which binary optimization and sparse optimization are two common ones. However, these problems are NP-hard and thus difficult…
This paper addresses a distributed convex optimization problem with a class of coupled constraints, which arise in a multi-agent system composed of multiple communities modeled by cliques. First, we propose a fully distributed…
In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…
Multiresolution topology optimization (MTO) methods involve decoupling of the design and analysis discretizations, such that a high-resolution design can be obtained at relatively low analysis costs. Recent studies have shown that the MTO…
The advent of advanced crystallographic techniques has shifted structural biology from static, single-conformer models toward probing protein dynamics. Extracting cooperative motions from temporally and spatially averaged electron density…
Mastering a skill generally relies on both hands-on experience from doers and insightful, high-level guidance by mentors. Will this strategy also work well for solving complex non-convex optimization problems? Here, a common gradient-based…
In this thesis we develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive…
Multi-frame methods improve monocular depth estimation over single-frame approaches by aggregating spatial-temporal information via feature matching. However, the spatial-temporal feature leads to accuracy degradation in dynamic scenes. To…
We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…
Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing the properties of a discrete crystal structure, such as those containing defects, that combine the accuracy of an atomistic (fully discrete) model with the…
Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local…
This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…
In this paper, a multi-objective approach for the design of composite data-driven mathematical models is proposed. It allows automating the identification of graph-based heterogeneous pipelines that consist of different blocks: machine…
Automatic Chemical Design is a framework for generating novel molecules with optimized properties. The original scheme, featuring Bayesian optimization over the latent space of a variational autoencoder, suffers from the pathology that it…
The capacity of automatically modeling photographic composition is valuable for many real-world machine vision applications such as digital photography, image retrieval, image understanding, and image aesthetics assessment. The triangle…