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 both the objective and constraints to jointly model the function values, gradients, and Hessian from only zero-order information. At each iteration, a local subproblem is constructed using the GP posterior estimates and solved to obtain a search direction. Crucially, the formulation of the subproblem explicitly incorporates uncertainty in both the function and derivative estimates, resulting in a tractable second-order cone program for high probability improvements under model uncertainty. A subsequent one-dimensional line search via constrained Thompson sampling selects the next evaluation point. Empirical results show that BayeSQPoutperforms state-of-the-art methods in specific high-dimensional settings. Our algorithm offers a principled and flexible framework that bridges classical optimization techniques with modern approaches to black-box optimization.

More recently, Newton-type methods using sparsified Hessian matrices have demonstrated promising results on OT computation, but there still remain a lot of unresolved open questions.

Motion planning is still an open problem for many disciplines, e.g., robotics, autonomous driving, due to their need for high computational resources that hinder

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This paper presents the Safe Sequential Quadratically Constrained Quadratic Programming (SS-QCQP) algorithm, a first-order method for smooth inequality-constrained nonconvex optimization that guarantees feasibility at every iteration. The method is derived from a continuous-time dynamical system whose vector field is obtained by solving a convex QCQP that enforces monotonic descent of the objective and forward invariance of the feasible set. The resulting continuous-time dynamics achieve an $O(1/t)$ convergence rate to first-order stationary points under standard constraint qualification conditions. We then propose a safeguarded Euler discretization with adaptive step-size selection that preserves this convergence rate while maintaining both descent and feasibility in discrete time. To enhance scalability, we develop an active-set variant (SS-QCQP-AS) that selectively enforces constraints near the boundary, substantially reducing computational cost without compromising theoretical guarantees. Numerical experiments on a multi-agent nonlinear optimal control problem demonstrate that SS-QCQP and SS-QCQP-AS maintain feasibility, exhibit the predicted convergence behavior, and deliver solution quality comparable to second-order solvers such as SQP and IPOPT.

Abstract-- We derive closed-form extensions of Riccati's recursions (both sequential [4] and parallel [7]) for solving dual-regularized LQR problems. We show how these methods can be used to solve general constrained, non-convex, discrete-time optimal control problems via a regularized interior point method, while guaranteeing that each primal step is a descent direction of an Augmented Barrier-Lagrangian merit function. We provide MIT -licensed implementations of our methods in C++ and JAX. Numerical optimal control, both real-time and offline, has found numerous application domains, ranging from trajectory optimization for robotics (e.g. for autonomous cars, unmanned aerial vehicles, legged robots) and airspace (e.g. Continuous-time optimal control problems, whose optimization variables are functions (thus infinite-dimensional) are typically converted into finite-dimensional optimization problems by either shooting (i.e.

Motion planning is still an open problem for many disciplines, e.g., robotics, autonomous driving, due to their need for high computational resources that hinder