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This paper proposes the algorithm NOWPAC (Nonlinear Optimization With Path-Augmented Constraints) for nonlinear constrained derivative-free optimization. The algorithm uses a trust region framework based on fully linear models for the…
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework…
This paper introduces new techniques for using convex optimization to fit input-output data to a class of stable nonlinear dynamical models. We present an algorithm that guarantees consistent estimates of models in this class when a small…
Unconstrained optimization problems are typically solved using iterative methods, which often depend on line search techniques to determine optimal step lengths in each iteration. This paper introduces a novel line search approach.…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear…
We present a derivative-based algorithm for nonlinearly constrained optimization problems that is tolerant of inaccuracies in the data. The algorithm solves a semi-smooth set of nonlinear equations that are equivalent to the first-order…
Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation…
This paper presents a novel quadratic programming (QP) approach for constrained control allocation that directly incorporates continuous-time actuator rate constraints without requiring slack variables. Over-actuated aircraft…
Generating time-optimal, collision-free trajectories for autonomous mobile robots involves a fundamental trade-off between guaranteeing safety and managing computational complexity. State-of-the-art approaches formulate spline-based motion…
In this paper, we propose a method that has foundations in the line search sequential quadratic programming paradigm for solving general nonlinear equality constrained optimization problems. The method employs a carefully designed modified…
We consider the problem of asynchronous stochastic optimization, where an optimization algorithm makes updates based on stale stochastic gradients of the objective that are subject to an arbitrary (possibly adversarial) sequence of delays.…
Sequential quadratic programming and sequential convex programming efficiently solve nonlinear programs (NLPs) by linearizing inner nonlinearities while preserving the outer convex structure. This paper introduces a sequential mixed-integer…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
We introduce a new method for solving nonlinear continuous optimization problems with chance constraints. Our method is based on a reformulation of the probabilistic constraint as a quantile function. The quantile function is approximated…
We introduce BayeSQP, a novel algorithm for general black-box optimization that merges the structure of sequential quadratic programming with concepts from Bayesian optimization. BayeSQP employs second-order Gaussian process surrogates for…
We propose a nonlinear model predictive control (NMPC) framework based on a direct optimal control method that ensures continuous-time constraint satisfaction and accurate evaluation of the running cost, without compromising computational…