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We study a class of constrained nonconvex-nonconcave minimax optimization problems in which the inner maximization involves potentially complex constraints. Under the assumption that the inner problem of a novel lifted minimax reformulation…
Many machine learning tasks, such as learning with invariance and policy evaluation in reinforcement learning, can be characterized as problems of learning from conditional distributions. In such problems, each sample $x$ itself is…
This paper addresses the problem of localization, which is inherently non-convex and non-smooth in a federated setting where the data is distributed across a multitude of devices. Due to the decentralized nature of federated environments,…
Translating machine learning algorithms into clinical applications requires addressing challenges related to interpretability, such as accounting for the effect of confounding variables (or metadata). Confounding variables affect the…
Non-convex optimization problems often arise from probabilistic modeling, such as estimation of posterior distributions. Non-convexity makes the problems intractable, and poses various obstacles for us to design efficient algorithms. In…
In this paper, we introduce a stochastic projected subgradient method for weakly convex (i.e., uniformly prox-regular) nonsmooth, nonconvex functions---a wide class of functions which includes the additive and convex composite classes. At a…
We present a trust-region-based adaptive finite-element algorithm for numerically solving a class of nonsmooth PDE-constrained optimization problems that includes problems with sparsifying regularizers and convex constraints. In particular,…
In federated distributed learning, the goal is to optimize a global training objective defined over distributed devices, where the data shard at each device is sampled from a possibly different distribution (a.k.a., heterogeneous or non…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
In this paper we present a finite element method for the direct transcription of constrained non-linear optimal control problems. We prove that our method converges of high order under mild assumptions. Our analysis uses a regularized…
The incorporation of generative models as regularisers within variational formulations for inverse problems has proven effective across numerous image reconstruction tasks. However, the resulting optimisation problem is often non-convex and…
Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…
We investigate a class of nonconvex optimization problems characterized by a feasible set consisting of level-bounded nonconvex regularizers, with a continuously differentiable objective. We propose a novel hybrid approach to tackle such…
We propose a method for efficiently incorporating constraints into a stochastic gradient Langevin framework for the training of deep neural networks. Constraints allow direct control of the parameter space of the model. Appropriately…
We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…
Optimal transportation of raw material from suppliers to customers is an issue arising in logistics that is addressed here with a continuous model relying on optimal transport theory. A physics informed neuralnetwork method is advocated…
Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…
Smoothing methods have become part of the standard tool set for the study and solution of nondifferentiable and constrained optimization problems as well as a range of other variational and equilibrium problems. In this note we synthesize…
We propose an algorithm to solve optimization problems constrained by partial (ordinary) differential equations under uncertainty, with almost sure constraints on the state variable. To alleviate the computational burden of high-dimensional…
This paper addresses the problem of nonconvex nonsmooth decentralised optimisation in multi-agent networks with undirected connected communication graphs. Our contribution lies in introducing an algorithmic framework designed for the…