nonlinear optimization

Optimistic Noise-Aware Sequential Quadratic Programming for Equality Constrained Optimization with Rank-Deficient Jacobians

  • Jiahao Shi
  • Baoyu Zhou
  • Albert S. Berahas
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , , ,

    We propose and analyze a sequential quadratic programming algorithm for minimizing a noisy nonlinear smooth function subject to noisy nonlinear smooth equality constraints. The algorithm uses a step decomposition strategy and, as a result, is robust to potential rank-deficiency in the constraints, allows for two different step size strategies, and has an early stopping mechanism. … Read more

    On liftings that improve convergence properties of Newton’s Method for Boundary Value Optimization Problems

  • Robert Lampel
  • Sebastian Sager
    • Categories Dynamic Programming, Nonlinear Optimization Tags , , ,

    The representation of a function in a higher-dimensional space is often referred to as lifting. Liftings can be used to reduce complexity. We are interested in the question of how liftings affect the local convergence of Newton’s method. We propose algorithms to construct liftings that potentially reduce the number of iterations via analysis of local … Read more

    An Interior-Point Algorithm for Continuous Nonlinearly Constrained Optimization with Noisy Function and Derivative Evaluations

  • Frank E. Curtis
  • Shima Dezfulian
  • Andreas Wächter
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization of Simulated Systems Tags , , , ,

    An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy values of the objective and constraint functions and their first-order derivatives are available. The algorithm is based on a combination of a previously … Read more

    Restarting nonlinear conjugate gradient methods

  • Morteza Kimiaei
  • Saman Babaie-Kafaki
  • Vyacheslav Kungurtsev
  • Mahsa Yousefi
    • Categories Nonlinear Optimization Tags , , , ,

    In unconstrained optimization, due to the nonlinearity of the objective function or rounding errors in finite precision arithmetic, it can happen that NaN or infinite step sizes appear in the nonlinear conjugate gradient (NCG) method, or otherwise the step violates the sufficient descent condition (SDC). In this case the conjugate gradient (CG) direction must often … Read more

    A Line Search Filter Sequential Adaptive Cubic Regularisation Algorithm for Nonlinearly Constrained Optimization

  • Yonggang Pei
  • Shaofang Song
  • Zhu Detong
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    In this paper, a sequential adaptive regularization algorithm using cubics (ARC) is presented to solve nonlinear equality constrained optimization. It is motivated by the idea of handling constraints in sequential quadratic programming methods. In each iteration, we decompose the new step into the sum of the normal step and the tangential step by using composite … Read more

    A Unified Funnel Restoration SQP Algorithm

  • David Kiessling
  • Sven Leyffer
  • Charlie Vanaret
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of four algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss-army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with … Read more

    A Two Stepsize SQP Method for Nonlinear Equality Constrained Stochastic Optimization

  • Michael J. O'Neill
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , ,

    We develop a Sequential Quadratic Optimization (SQP) algorithm for minimizing a stochastic objective function subject to deterministic equality constraints. The method utilizes two different stepsizes, one which exclusively scales the component of the step corrupted by the variance of the stochastic gradient estimates and a second which scales the entire step. We prove that this … Read more

    Refining asymptotic complexity bounds for nonconvex optimization methods, including why steepest descent is o(eps^{-2}) rather than O(eps^{-2})

  • Serge Gratton
  • Chee-Khian Sim
  • Philippe L. Toint
    • Categories Nonlinear Optimization Tags ,

    We revisit the standard “telescoping sum” argument ubiquitous in the final steps of analyzing evaluation complexity of algorithms for smooth nonconvex optimization, and obtain a refined formulation of the resulting bound as a function of the requested accuracy eps. While bounds obtained using the standard argument typically are of the form \(O(\epsilon^{-\alpha})\) for some positive … Read more

    Modified Line Search Sequential Quadratic Methods for Equality-Constrained Optimization with Unified Global and Local Convergence Guarantees

  • Albert S. Berahas
  • Raghu Bollapragada
  • Jiahao Shi
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Other Topics Tags , ,

    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 line search strategy that utilizes second-order information of both the objective and constraint functions, as required, to mitigate the Maratos effect. Contrary … Read more

    Unifying nonlinearly constrained nonconvex optimization

  • Charlie Vanaret
  • Sven Leyffer
    • Categories Constrained Nonlinear Optimization, Optimization Software Benchmark Tags , , , , , , , , ,

    Derivative-based iterative methods for nonlinearly constrained non-convex optimization usually share common algorithmic components, such as strategies for computing a descent direction and mechanisms that promote global convergence. Based on this observation, we introduce an abstract framework based on four common ingredients that describes most derivative-based iterative methods and unifies their workflows. We then present Uno, … Read more