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Recent strides in nonlinear model predictive control (NMPC) underscore a dependence on numerical advancements to efficiently and accurately solve large-scale problems. Given the substantial number of variables characterizing typical…
Traditional approaches to portfolio optimization, often rooted in Modern Portfolio Theory and solved via quadratic programming or evolutionary algorithms, struggle with scalability or flexibility, especially in scenarios involving complex…
Standard Markov decision process (MDP) and reinforcement learning algorithms optimize the policy with respect to the expected gain. We propose an algorithm which enables to optimize an alternative objective: the probability that the gain is…
In this paper, we utilize stochastic optimization to reduce the space complexity of convex composite optimization with a nuclear norm regularizer, where the variable is a matrix of size $m \times n$. By constructing a low-rank estimate of…
We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…
We provide performance guarantees for a variant of simulation-based policy iteration for controlling Markov decision processes that involves the use of stochastic approximation algorithms along with state-of-the-art techniques that are…
Optimization problems constrained by partial differential equations (PDEs) naturally arise in scientific computing, as those constraints often model physical systems or the simulation thereof. In an implicitly constrained approach, the…
Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity…
We propose a novel stochastic approximation algorithm, termed PMQSopt, for solving weakly convex stochastic optimization problems involving expectation-valued functions. The algorithm is constructed by integrating the proximal method of…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…
Group Relative Policy Optimization (GRPO) has become a standard approach for training mathematical reasoning models; however, its reliance on multiple completions per prompt makes training computationally expensive. Although recent work has…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Model predictive control (MPC) is increasingly being considered for control of fast systems and embedded applications. However, the MPC has some significant challenges for such systems. Its high computational complexity results in high…
Stochastic rounding (SR) is a probabilistic method used to round numbers to floating-point and fixed-point representations. In length $n$ summation, the worst-case error of SR grows as $\sqrt{n}$ with high probability, unlike for standard…
We develop two iterative algorithms for solving the low rank phase retrieval (LRPR) problem. LRPR refers to recovering a low-rank matrix $\X$ from magnitude-only (phaseless) measurements of random linear projections of its columns. Both…
Regularization has long been utilized to learn sparsity in deep neural network pruning. However, its role is mainly explored in the small penalty strength regime. In this work, we extend its application to a new scenario where the…
In genetical genomics studies, it is important to jointly analyze gene expression data and genetic variants in exploring their associations with complex traits, where the dimensionality of gene expressions and genetic variants can both be…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…