Related papers: Remarks on "Successive Convexification: A Superlin…
We study the problem of online convex optimization (OCO) under unknown linear constraints that are either static, or stochastically time-varying. For this problem, we introduce an algorithm that we term Optimistically Safe OCO (OSOCO) and…
We address black-box convex optimization problems, where the objective and constraint functions are not explicitly known but can be sampled within the feasible set. The challenge is thus to generate a sequence of feasible points converging…
Sequential Convex Programming (SCP) has recently seen a surge of interest as a tool for trajectory optimization. However, most available methods lack rigorous performance guarantees and they are often tailored to specific optimal control…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
Reliable and efficient trajectory generation methods are a fundamental need for autonomous dynamical systems of tomorrow. The goal of this article is to provide a comprehensive tutorial of three major convex optimization-based trajectory…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
We propose an algorithm that produces a non-decreasing sequence of subsolutions for a class of optimal control problems distinguished by the property that the associated Bellman operators preserve convexity. In addition to a theoretical…
This paper presents an extension to the nonlinear Model Predictive Control for Tracking scheme able to guarantee convergence even in cases of non-convex output admissible sets. This is achieved by incorporating a convexifying homeomorphism…
We propose a novel continuous-time algorithm for inequality-constrained convex optimization inspired by proportional-integral control. Unlike the popular primal-dual gradient dynamics, our method includes a proportional term to control the…
While traditional distributionally robust optimization (DRO) aims to minimize the maximal risk over a set of distributions, Agarwal and Zhang (2022) recently proposed a variant that replaces risk with excess risk. Compared to DRO, the new…
This paper considers online convex optimization (OCO) with stochastic constraints, which generalizes Zinkevich's OCO over a known simple fixed set by introducing multiple stochastic functional constraints that are i.i.d. generated at each…
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…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…
Despite the recent development in machine learning, most learning systems are still under the concept of "black box", where the performance cannot be understood and derived. With the rise of safety and privacy concerns in public, designing…
Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…
Convex optimization is crucial in controlling legged robots, where stability and optimal control are vital. Many control problems can be formulated as convex optimization problems, with a convex cost function and constraints capturing…
In this paper, we propose a predictor-corrector type Consensus Based Optimization (CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the…
We study the problem of safe online convex optimization, where the action at each time step must satisfy a set of linear safety constraints. The goal is to select a sequence of actions to minimize the regret without violating the safety…
We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…
We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…