Victor M. Zavala

A Sequential Algorithm for Solving Nonlinear Optimization Problems with Chance Constraints

  • Frank E. Curtis
  • Victor M. Zavala
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , , ,

    An algorithm is presented for solving nonlinear optimization problems with chance constraints, i.e., those in which a constraint involving an uncertain parameter must be satisfied with at least a minimum probability. In particular, the algorithm is designed to solve cardinality-constrained nonlinear optimization problems that arise in sample average approximations of chance-constrained problems, as well as … Read more

    pyomo.dae: A Modeling and Automatic Discretization Framework for Optimization with Differential and Algebraic Equations

  • Lorenz T. Biegler
  • Jean-Paul Watson
  • Victor M. Zavala
  • Bethany Nicholson
  • John D. Siirola
    • Categories Modeling Languages and Systems, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags , , , ,

    We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http: //www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, … Read more

    A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties

  • Mihai Anitescu
  • John Birge
  • Kibaek Kim
  • Victor M. Zavala
    • Categories Applications - OR and Management Sciences, Convex and Nonsmooth Optimization, Stochastic Programming

    We argue that deterministic market clearing formulations introduce arbitrary distortions between day-ahead and expected real-time prices that bias economic incentives and block diversi cation. We extend and analyze the stochastic clearing formulation proposed by Pritchard et al. (2010) in which the social surplus function induces penalties between day-ahead and real-time quantities. We prove that the formulation … Read more

    Nonlinear Programming Strategies on High-Performance Computers

  • Naiyuan Chiang
  • Carl D. Laird
  • Victor M. Zavala
  • Jia Kang
    • Categories Constrained Nonlinear Optimization, Parallel Algorithms, Systems governed by Differential Equations Optimization

    We discuss structured nonlinear programming problems arising in control applications, and we review software and hardware capabilities that enable the efficient exploitation of such structures. We focus on linear algebra parallelization strategies and discuss how these interact and influence high-level algorithmic design elements required to enforce global convergence and deal with negative curvature in a … Read more

    Algorithmic innovations and software for the dual decomposition method applied to stochastic mixed-integer programs

  • Kibaek Kim
  • Victor M. Zavala
    • Categories Optimization Software and Modeling Systems, Parallel Algorithms, Stochastic Programming

    We develop algorithmic innovations for the dual decomposition method to address two-stage stochastic programs with mixed-integer recourse and provide a parallel software implementation that we call DSP. Our innovations include the derivation of valid inequalities that tighten Lagrangian subproblems and that allow the guaranteed recovery of feasible solutions for problems without (relative) complete recourse. We … Read more

    Bridging the Gap Between Multigrid, Hierarchical, and Receding-Horizon Control

  • Victor M. Zavala
    • Categories Distributed Control, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    We analyze the structure of the Euler-Lagrange conditions of a lifted long-horizon optimal control problem. The analysis reveals that the conditions can be solved by using block Gauss-Seidel schemes and we prove that such schemes can be implemented by solving sequences of short-horizon problems. The analysis also reveals that a receding-horizon control scheme is equivalent … Read more

    Clustering-Based Preconditioning for Stochastic Programs

  • Yankai Cao
  • Carl D. Laird
  • Victor M. Zavala
    • Categories Linear Programming, Quadratic Programming, Stochastic Programming

    We present a clustering-based preconditioning strategy for KKT systems arising in stochastic programming within an interior-point framework. The key idea is to perform adaptive clustering of scenarios (inside-the-solver) based on their influence on the problem as opposed to cluster scenarios based on problem data alone, as is done in existing (outside-thesolver) approaches. We derive spectral … Read more

    An Inertia-Free Filter Line-Search Algorithm for Large-Scale Nonlinear Programming

  • Naiyuan Chiang
  • Victor M. Zavala
    • Categories Nonlinear Optimization, Optimization of Systems modeled by PDEs, Stochastic Programming Tags , , , ,

    We present a filter line-search algorithm that does not require inertia information about the linear system to ensure global convergence. The proposed approach performs curvature tests along the search step to ensure descent. This feature permits more modularity in the linear algebra, enabling the use of a wider range of iterative and decomposition strategies. We … Read more

    Scalable Nonlinear Programming Via Exact Differentiable Penalty Functions and Trust-Region Newton Methods

  • Mihai Anitescu
  • Victor M. Zavala
    • Categories Control Applications, Nonlinear Optimization Tags , , , , ,

    We present an approach for nonlinear programming (NLP) based on the direct minimization of an exact di erentiable penalty function using trust-region Newton techniques. As opposed to existing algorithmic approaches to NLP, the approach provides all the features required for scalability: it can eciently detect and exploit directions of negative curvature, it is superlinearly convergent, and … Read more

    Stochastic Optimization Approach to Water Management in Cooling-Constrained Power Plants

  • Emil M. Constantinescu
  • Victor M. Zavala
  • Urmila Diwekar
  • Juan M. Salazar
    • Categories Applications - OR and Management Sciences, Constrained Nonlinear Optimization, Stochastic Programming

    We propose a stochastic optimization framework to perform water management in coolingconstrained power plants. The approach determines optimal set-points to maximize power output in the presence of uncertain weather conditions and water intake constraints. Weather uncertainty is quantified in the form of ensembles using the state-of-the-art numerical weather prediction model WRF. The framework enables us … Read more