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In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
A stochastic linear quadratic (LQ) optimal control problem with a pointwise linear equality constraint on the terminal state is considered. A strong Lagrangian duality theorem is proved under a uniform convexity condition on the cost…
In this work we focus on efficient heuristics for solving a class of stochastic planning problems that arise in a variety of business, investment, and industrial applications. The problem is best described in terms of future buy and sell…
This paper presents an efficient and comprehensive MATLAB code to solve two-dimensional structural topology optimization problems, including minimum mean compliance, compliant mechanism synthesis and multi-load compliance problems. The…
The Maximum Flow Problem with Conflict Constraints is a generalization that adds conflict constraints to a classical optimization problem on networks used to model several real-world applications. In the last few years several approaches,…
Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…
A central problem in business concerns the optimal allocation of limited resources to a set of available tasks, where the payoff of these tasks is inherently uncertain. In credit card fraud detection, for instance, a bank can only assign a…
In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…
A recent article introduced thecontinuous stochastic gradient method (CSG) for the efficient solution of a class of stochastic optimization problems. While the applicability of known stochastic gradient type methods is typically limited to…
Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…
An optimization algorithm for a group of nonsmooth nonconvex problems inspired by two-stage stochastic programming problems is proposed. The main challenges for these problems include (1) the problems lack the popular lower-type properties…
Navigating a collision-free and optimal trajectory for a robot is a challenging task, particularly in environments with moving obstacles such as humans. We formulate this problem as a stochastic optimal control problem. Since solving the…
Continual learning is inherently a constrained learning problem. The goal is to learn a predictor under a no-forgetting requirement. Although several prior studies formulate it as such, they do not solve the constrained problem explicitly.…
In this paper, we discuss the ambiguous chance constrained based portfolio optimization problems, in which the perturbations associated with the input parameters are stochastic in nature, but their distributions are not known precisely. We…
We consider regression problems with binary weights. Such optimization problems are ubiquitous in quantized learning models and digital communication systems. A natural approach is to optimize the corresponding Lagrangian using variants of…
We study a stochastic recursive optimal control problem in which the cost functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Some of the economic and financial optimization…
Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…
Linear complementarity problems are a powerful tool for modeling many practically relevant situations such as market equilibria. They also connect many sub-areas of mathematics like game theory, optimization, and matrix theory. Despite…
In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…