Related papers: Multi-extremum optimization in lens design: naviga…
Computing saddle points with a prescribed Morse index on potential energy surfaces is crucial for characterizing transition states for nosie-induced rare transition events in physics and chemistry. Many numerical algorithms for this type of…
Despite the fact that the loss functions of deep neural networks are highly non-convex, gradient-based optimization algorithms converge to approximately the same performance from many random initial points. One thread of work has focused on…
Computer vision is one of the most active research fields in information technology today. Giving machines and robots the ability to see and comprehend the surrounding world at the speed of sight creates endless potential applications and…
The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to $c$-conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes…
In this paper, we propose a Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The objective function of the problem under consideration is given by…
In this paper, by designing a normalized nonmonotone search strategy with the Barzilai--Borwein-type step-size, a novel local minimax method (LMM), which is a globally convergent iterative method, is proposed and analyzed to find multiple…
Many offline unsupervised change point detection algorithms rely on minimizing a penalized sum of segment-wise costs. We extend this framework by proposing to minimize a sum of discrepancies between segments. In particular, we propose to…
Optimization seeks extremal points in a function. When there are superextensively many optima, optimization algorithms are liable to get stuck. Under these conditions, generic algorithms tend to find marginal optima, which have many nearly…
The MM principle is a device for creating optimization algorithms satisfying the ascent or descent property. The current survey emphasizes the role of the MM principle in nonlinear programming. For smooth functions, one can construct an…
In this article, we dwell into the class of so-called ill-posed Linear Inverse Problems (LIP) which simply refers to the task of recovering the entire signal from its relatively few random linear measurements. Such problems arise in a…
In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods…
Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…
This paper formulates the problem of Extremum Seeking for optimization of cost functions defined on Riemannian manifolds. We extend the conventional extremum seeking algorithms for optimization problems in Euclidean spaces to optimization…
Many real world applications can be framed as multi-objective optimization problems, where we wish to simultaneously optimize for multiple criteria. Bayesian optimization techniques for the multi-objective setting are pertinent when the…
The broad success of theoretical and experimental quantum optimal control is intimately connected to the topology of the underlying control landscape. For several common quantum control goals, including the maximization of an observable…
We propose two deep neural network-based methods for solving semi-martingale optimal transport problems. The first method is based on a relaxation/penalization of the terminal constraint, and is solved using deep neural networks. The second…
Most camera lens systems are designed in isolation, separately from downstream computer vision methods. Recently, joint optimization approaches that design lenses alongside other components of the image acquisition and processing pipeline…
Recent analyses of certain gradient descent optimization methods have shown that performance can degrade in some settings - such as with stochasticity or implicit momentum. In deep reinforcement learning (Deep RL), such optimization methods…
Multi-Agent Path Finding (MAPF) is an NP-hard problem with applications in warehouse automation and multi-robot coordination. Learning-based MAPF solvers offer fast and scalable planning but often produce feasible trajectories that contain…
We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum,…