nonlinear optimization

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

    S2MPJ and CUTEst optimization problems for Matlab, Python and Julia

  • Serge Gratton
  • Philippe L. Toint
    • Categories Nonlinear Optimization, Optimization Software Benchmark Tags , , , , ,

    A new decoder for the SIF test problems of the \cutest\ collection is described, which produces problem files allowing the computation of values and derivatives of the objective function and constraints of most \cutest\ problems directly within “native” Matlab, Python or Julia, without any additional installation or interfacing with MEX files or Fortran programs. When … Read more

    On the global convergence of a general class of augmented Lagrangian methods

  • Ernesto G. Birgin
  • Gabriel Haeser
  • Nelson Maculan
  • Lennin Mallma Ramirez
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    In [E. G. Birgin, R. Castillo and J. M. Martínez, Computational Optimization and Applications 31, pp. 31-55, 2005], a general class of safeguarded augmented Lagrangian methods is introduced which includes a large number of different methods from the literature. Besides a numerical comparison including 65 different methods, primal-dual global convergence to a KKT point is … Read more

    A Proximal-Gradient Method for Constrained Optimization

  • Daniel P. Robinson
  • Yutong Dai
  • Xiaoyi Qu
    • Categories Nonlinear Optimization, Optimization in Data Science Tags , , , , ,

    We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be viewed as an extension of the well-known proximal-gradient method that is applicable when constraints are not present. To account for nonlinear … Read more

    Safeguarded augmented Lagrangian algorithms with scaled stopping criterion for the subproblems

  • Ernesto G. Birgin
  • Gabriel Haeser
  • José Mario Martínez
    • Categories Nonlinear Optimization Tags , , ,

    At each iteration of the Safeguarded Augmented Lagrangian algorithm Algencan, a bound-constrained subproblem consisting of the minimization of the Powell-Hestenes-Rockafellar augmented Lagrangian function is considered, for which a minimizer with tolerance tending to zero is sought. More precisely, a point that satisfies a subproblem first-order necessary optimality condition with tolerance tending to zero is required. … Read more

    Sequential Quadratic Optimization for Stochastic Optimization with Deterministic Nonlinear Inequality and Equality Constraints

  • Frank E. Curtis
  • Daniel P. Robinson
  • Baoyu Zhou
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Programming Tags , ,

    A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is tractable to evaluate constraint function and derivative values in each iteration, but it is intractable to evaluate the objective function or … Read more

    On the paper “Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem”

  • Luís Felipe Bueno
  • Gabriel Haeser
  • Oliver Kolossoski
    • Categories Nonlinear Optimization Tags , ,

    In the paper [Torrealba, E.M.R. et al. Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem. EJOR, 299(1) 46–59, 2021] an augmented Lagrangian algorithm was proposed for resource allocation problems with the intriguing characteristic that instead of solving the box-constrained augmented Lagrangian subproblem, they propose projecting the solution of the unconstrained subproblem onto … Read more

    Gas Transport Network Optimization: Mixed-Integer Nonlinear Models

  • Falk M. Hante
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering Tags , , ,

    Although modern societies strive towards energy systems that are entirely based on renewable energy carriers, natural gas is still one of the most important energy sources. This became even more obvious in Europe with Russia’s 2022 war against the Ukraine and the resulting stop of gas supplies from Russia. Besides that it is very important … Read more