Related papers: Submodularization for Quadratic Pseudo-Boolean Opt…
The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…
With the rapid advancement of quantum computing, Quantum Approximate Optimization Algorithm (QAOA) is considered as a promising candidate to demonstrate quantum supremacy, which exponentially solves a class of Quadratic Unconstrained Binary…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…
In this paper, we investigate the possibility of improving the performance of multi-objective optimization solution approaches using machine learning techniques. Specifically, we focus on multi-objective binary linear programs and employ…
We discuss a unified approach to stochastic optimization of pseudo-Boolean objective functions based on particle methods, including the cross-entropy method and simulated annealing as special cases. We point out the need for auxiliary…
Neural operators have emerged as data-driven surrogates for solving partial differential equations (PDEs), and their success hinges on efficiently modeling the long-range, global coupling among spatial points induced by the underlying…
The aim of sparse approximation is to estimate a sparse signal according to the measurement matrix and an observation vector. It is widely used in data analytics, image processing, and communication, etc. Up to now, a lot of research has…
Many recent advances in computer vision have demonstrated the impressive power of dense and nonsubmodular energy functions in solving visual labeling problems. However, minimizing such energies is challenging. None of existing techniques…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
The problem of non-monotone $k$-submodular maximization under a knapsack constraint ($\kSMK$) over the ground set size $n$ has been raised in many applications in machine learning, such as data summarization, information propagation, etc.…
This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size $n$ subject to a knapsack constraint, $\mathsf{DLA}$ and…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
Stochastic Bilevel optimization usually involves minimizing an upper-level (UL) function that is dependent on the arg-min of a strongly-convex lower-level (LL) function. Several algorithms utilize Neumann series to approximate certain…
Blind Super-Resolution (SR) usually involves two sub-problems: 1) estimating the degradation of the given low-resolution (LR) image; 2) super-resolving the LR image to its high-resolution (HR) counterpart. Both problems are ill-posed due to…
With the extensive application of submodularity, its generalizations are constantly being proposed. However, most of them are tailored for special problems. In this paper, we focus on quasi-submodularity, a universal generalization, which…
In this thesis I explore challenging discrete energy minimization problems that arise mainly in the context of computer vision tasks. This work motivates the use of such "hard-to-optimize" non-submodular functionals, and proposes methods…
The local convergence of alternating optimization methods with overrelaxation for low-rank matrix and tensor problems is established. The analysis is based on the linearization of the method which takes the form of an SOR iteration for a…
Commonly used in computer vision and other applications, robust PCA represents an algorithmic attempt to reduce the sensitivity of classical PCA to outliers. The basic idea is to learn a decomposition of some data matrix of interest into…
In recent years, a variety of gradient-based methods have been developed to solve Bi-Level Optimization (BLO) problems in machine learning and computer vision areas. However, the theoretical correctness and practical effectiveness of these…
In this paper, we propose SubLoRA, a rank determination method for Low-Rank Adaptation (LoRA) based on submodular function maximization. In contrast to prior approaches, such as AdaLoRA, that rely on first-order (linearized) approximations…