Related papers: Anytime-Feasible First-Order Optimization via Safe…
Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has…
Large-scale constrained optimization problems are at the core of many tasks in control, signal processing, and machine learning. Notably, problems with functional constraints arise when, beyond a performance{\nobreakdash-}centric goal…
We analyze worst-case convergence guarantees of first-order optimization methods over a function class extending that of smooth and convex functions. This class contains convex functions that admit a simple quadratic upper bound. Its study…
We present successive convexification, a real-time-capable solution method for nonconvex trajectory optimization, with continuous-time constraint satisfaction and guaranteed convergence, that only requires first-order information. The…
We provide the first study of the problem of finding differentially private (DP) second-order stationary points (SOSP) in stochastic (non-convex) minimax optimization. Existing literature either focuses only on first-order stationary points…
In this paper, we present a stabilized sequential quadratic semidefinite programming (SQSDP) method for nonlinear semidefinite programming (NSDP) problems and prove its local convergence. The stabilized SQSDP method is originally developed…
Stochastic sequential quadratic optimization (SQP) methods for solving continuous optimization problems with nonlinear equality constraints have attracted attention recently, such as for solving large-scale data-fitting problems subject to…
This study considers the control problem with signal temporal logic (STL) specifications. Prior works have adopted smoothing techniques to address this problem within a feasible time frame and solve the problem by applying sequential…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…
In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for…
Optimal Power Flow (OPF) can be modeled as a non-convex Quadratically Constrained Quadratic Program (QCQP). Our purpose is to solve OPF to global optimality. To this end, we specialize the Mixed-Integer Quadratic Convex Reformulation method…
In this paper, we consider the problem of minimum-time optimal control for a dynamical system with initial state uncertainties and propose a sequential convex programming (SCP) solution framework. We seek to minimize the expected terminal…
Invex programs are a special kind of non-convex problems which attain global minima at every stationary point. While classical first-order gradient descent methods can solve them, they converge very slowly. In this paper, we propose new…
In this paper, we present novel randomized algorithms for solving saddle point problems whose dual feasible region is given by the direct product of many convex sets. Our algorithms can achieve an ${\cal O}(1/N)$ and ${\cal O}(1/N^2)$ rate…
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…
This paper develops a generalization of the line-search sequential quadratic programming (SQP) algorithm with $\ell_1$-merit function that uses objective and constraint function approximations with tunable accuracy to solve smooth…
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…
Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that…
Distributed optimization has gained significant attention in recent years, primarily fueled by the availability of a large amount of data and privacy-preserving requirements. This paper presents a fixed-time convergent optimization…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…