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We obtain the variational equations for backward stochastic differential equations in recursive stochastic optimal control problems, and then get the maximum principle which is novel. The control domain need not be convex, and the generator…

Optimization and Control · Mathematics 2015-07-14 Mingshang Hu

We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…

Optimization and Control · Mathematics 2008-03-07 Ivar Ekeland , Santiago Moreno

We introduce a new framework for optimal routing and arbitrage in AMM driven markets. This framework improves on the original best-practice convex optimization by restricting the search to the boundary of the optimal space. We can…

Mathematical Finance · Quantitative Finance 2025-02-13 Stefan Loesch , Mark Bentley Richardson

Time-varying non-convex continuous-valued non-linear constrained optimization is a fundamental problem. We study conditions wherein a momentum-like regularising term allow for the tracking of local optima by considering an ordinary…

Optimization and Control · Mathematics 2019-09-18 Olivier Massicot , Jakub Marecek

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

Optimization and Control · Mathematics 2015-08-21 Bram L. Gorissen

In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing…

Data Structures and Algorithms · Computer Science 2024-11-05 Aditya Pillai , Gabriel Ponte , Marcia Fampa , Jon Lee , and Mohit Singh , Weijun Xie

Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work…

Optimization and Control · Mathematics 2021-06-17 Linchuan Wei , Andres Gomez , Simge Kucukyavuz

Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…

Optimization and Control · Mathematics 2019-07-19 Timothy C. Y. Chan , Neal Kaw

Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…

Machine Learning · Computer Science 2016-11-18 Ruoyu Sun , Zhi-Quan Luo

This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…

Optimization and Control · Mathematics 2019-11-21 Danylo Malyuta , Behcet Acikmese

In a reinforcement learning (RL) framework, we study the exploratory version of the continuous time expected utility (EU) maximization problem with a portfolio constraint that includes widely-used financial regulations such as short-selling…

Mathematical Finance · Quantitative Finance 2024-12-17 Huy Chau , Duy Nguyen , Thai Nguyen

Reinforcement Learning is a powerful framework for training agents to navigate different situations, but it is susceptible to changes in environmental dynamics. However, solving Markov Decision Processes that are robust to changes is…

Machine Learning · Computer Science 2024-06-21 Etash Kumar Guha

This paper investigates reverse auctions that involve continuous values of different types of goods, general nonconvex constraints, and second stage costs. We seek to design the payment rules and conditions under which coalitions of…

Computer Science and Game Theory · Computer Science 2021-07-14 Orcun Karaca , Pier Giuseppe Sessa , Neil Walton , Maryam Kamgarpour

We study the problem of minimizing non-convex functionals on the space of probability measures, regularized by the relative entropy (KL divergence) with respect to a fixed reference measure, as well as the corresponding problem of solving…

Optimization and Control · Mathematics 2025-10-16 Razvan-Andrei Lascu , Mateusz B. Majka

Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…

Optimization and Control · Mathematics 2026-01-27 Anran Li , John P. Swensen , Mehdi Hosseinzadeh

Proximal operators with affine constraints arise in numerous models in nonconvex projection, composite optimization, and structured regularization. However, their efficient computation remains challenging due to the simultaneous presence of…

Optimization and Control · Mathematics 2026-03-02 Di Hou , Tianyun Tang , Kim-Chuan Toh , Shiwei Wang

We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the…

Optimization and Control · Mathematics 2023-05-09 Lintao Ye , Zhi-Wei Liu , Ming Chi , Vijay Gupta

We propose a distributionally robust principal agent formulation, which generalizes some common variants of worst-case and Bayesian principal agent problems. We construct a theoretical framework to certify whether any surjective contract…

Theoretical Economics · Economics 2024-01-17 Peter Zhang

We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward…

Optimization and Control · Mathematics 2024-05-07 Nicola Bastianello , Andrea Simonetto , Ruggero Carli

We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. Approximate solutions can be found by solving a convexified version of the problem, in which…

Optimization and Control · Mathematics 2016-01-12 Madeleine Udell , Stephen Boyd