nonlinear optimization

An Adaptive Augmented Lagrangian Method for Deterministic and Stochastic Nonconvex Optimization

Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , ,

We present an inexact Augmented Lagrangian algorithm for solving nonlinear, non-convex optimization problems. Unlike most recently proposed Augmented Lagrangian methods with worst-case complexity guarantees, we utilize adaptive penalty parameter updates and full dual stepsizes. We show that the method matches the best known worst-case complexity results for Augmented Lagrangian methods (up to logarithmic factors) when … Read more

Combining Reinforcement Learning with Arc-search Interior-Point Method for Path Planning

Categories Constrained Nonlinear Optimization, Control Applications, Nonlinear Optimization Tags , , ,

Path planning in environments containing obstacles has numerous practical applications. The problem is challenging because it is inherently nonlinear and nonconvex. Consequently, a variety of techniques have been developed to address this problem, among which machine learning and optimal control (or optimization) have emerged as two prominent approaches. In general, machine learning methods do not … Read more

An arc-search interior-point algorithm for nonlinear constrained optimization

Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , ,

This paper proposes a new arc-search interior-point algorithm for the nonlinear constrained optimization problem. The proposed algorithm uses the second-order derivatives to construct a search arc that approaches the optimizer. Because the arc stays in the interior set longer than any straight line, it is expected that the scheme will generate a better new iterate … Read more

A Minimal-Gradient Subspace Method for Unconstrained Optimization

Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

We propose a minimal-gradient subspace method for unconstrained optimization. For strictly convex quadratics, conjugate gradient can be interpreted as exact minimization over a two-dimensional affine subspace. We use the same reduced subspace in the nonlinear case, but compute a trial step by minimizing a local model of the next gradient norm. For SPD quadratics, every … Read more

A Data-Assimilation-Augmented Optimization Framework for Parameter Estimation in Dynamical Systems

Categories Control Applications, Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

Parameter estimation in nonlinear dynamical systems from observational data is a fundamental inverse problem with applications in many disciplines such as epidemiology, systems biology, climate science, and related fields. In practice, this is further complicated by the fact that observational data are often noisy, sparse, and available only for a subset of the state variables. … Read more

D-optimal partitioning: design of experiments under heterogeneous treatment effects

Categories Combinatorial Optimization, Nonlinear Optimization, Optimization in Data Science Tags , , , ,

Modern experimentation in business and public policy often studies targeted interventions whose effects depend on the heterogeneous attributes of individuals. We examine heterogeneous treatment effects through the lens of optimal design of experiments, which allocates treatment decisions to maximize the precision of estimated treatment-covariate interactions. We introduce the D-optimal partitioning problem for balancing the information … Read more

Distributionally Robust Optimization with General Uncertainty Structure

Categories Nonlinear Optimization, Robust Optimization, Stochastic Programming Tags , , , , , ,

We develop an exact solution framework for a broad class of Distributionally Robust Optimization (DRO) problems with general uncertainty structure. Within the class of moment- and confidence-set-based ambiguity sets, existing exact methods are largely limited to max-of-affine functions under ambiguity sets with strictly nested confidence sets. To enlarge this scope while preserving tractability, we introduce … Read more

Finite-Sample Optimality and Constraint Satisfaction: Learning-Based Optimal Control in Dynamic Dispatch Networks

Categories Data Science Theory, Production and Logistics, Transportation Tags , ,

Dynamic dispatch networks in logistics and transportation require real-time, constraint-aware decision-making under stochastic demand. This paper bridges mathematical optimization, optimal control theory, and reinforcement learning by establishing non-asymptotic theoretical guarantees for learning-based optimal control in constrained stochastic dispatch systems. We formulate the problem as a constrained Markov decision process, enforce feasibility via a projection-based policy … Read more

Complexity of an inexact stochastic SQP algorithm for equality constrained optimization

Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , ,

In this paper, we consider nonlinear optimization problems with a stochastic objective function and deterministic equality constraints. We propose an inexact two-stepsize stochastic sequential quadratic programming (SQP) algorithm and analyze its worst-case complexity under mild assumptions. The method utilizes a step decomposition strategy and handles stochastic gradient estimates by assigning different stepsizes to different components … Read more

A Multi-Secant Limited-Memory BFGS Method

Categories Unconstrained Optimization Tags ,

We develop multi-secant BFGS-like quasi-Newton updating scheme, which adaptively selects the number of imposed secant conditions and naturally preserves positivity of approximated Hessian. Compact representation and respective limited-memory formulation are also derived. Numerical stability is assured via unconventional damping technique, which symmetrically handles coordinate and gradient differences. Practical relevance of proposed method is demonstrated via … Read more