Related papers: Remarks on "Successive Convexification: A Superlin…
This paper presents the SCvx algorithm, a successive convexification algorithm designed to solve non-convex constrained optimal control problems with global convergence and superlinear convergence-rate guarantees. The proposed algorithm can…
In this paper, we extend our previous results and formally propose the SCvx-fast algorithm, a new addition to the Successive Convexification algorithmic framework. The said algorithm solves non-convex optimal control problems with specific…
This paper proposes a new algorithm that solves non-convex optimal control problems with a theoretical guarantee for global convergence to a feasible local solution of the original problem. The proposed algorithm extends the recently…
This paper presents a Successive Convexification ($ \texttt{SCvx} $) algorithm to solve a class of non-convex optimal control problems with certain types of state constraints. Sources of non-convexity may include nonlinear dynamics and…
Lossless Convexification (LCvx) is a convexification technique that transforms a class of nonconvex optimal control problems$\unicode{x2013}$where the nonconvexity arises from a lower bound on the control norm$\unicode{x2013}$into…
In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
We consider stochastic convex optimization with a strongly convex (but not necessarily smooth) objective. We give an algorithm which performs only gradient updates with optimal rate of convergence.
This paper presents an algorithm to solve non-convex optimal control problems, where non-convexity can arise from nonlinear dynamics, and non-convex state and control constraints. This paper assumes that the state and control constraints…
It is widely recognized in modern machine learning practice that access to a diverse set of tasks can enhance performance across those tasks. This observation suggests that, unlike in general multi-objective optimization, the objectives in…
In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full…
Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables…
This paper presents auto-tuned primal-dual successive convexification (Auto-SCvx), an algorithm designed to reliably achieve dynamically-feasible trajectory solutions for constrained hypersonic reentry optimal control problems across a…
The majorization-minimization (MM) principle is an extremely general framework for deriving optimization algorithms. It includes the expectation-maximization (EM) algorithm, proximal gradient algorithm, concave-convex procedure, quadratic…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
We prove convergence of a single time-scale stochastic subgradient method with subgradient averaging for constrained problems with a nonsmooth and nonconvex objective function having the property of generalized differentiability. As a tool…
Lately, a novel swarm intelligence model, namely the consensus-based optimization (CBO) algorithm, was introduced to deal with the global optimization problems. Limited by the conditions of Ito's formula, the convergence analysis of the…
Inverse optimization (IO) aims to determine optimization model parameters from observed decisions. However, IO is not part of a data scientist's toolkit in practice, especially as many general-purpose machine learning packages are widely…
A fundamental issue at the core of trajectory optimization on smooth manifolds is handling the implicit manifold constraint within the dynamics. The conventional approach is to enforce the dynamic model as a constraint. However, we show…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…