Reliable Frequency Regulation through Vehicle-to-Grid: Encoding Legislation with Robust Constraints

  • Dirk Lauinger
  • François Vuille
  • Daniel Kuhn
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Robust Optimization Tags , , , , ,

    Problem definition: Vehicle-to-grid increases the low utilization rate of privately owned electric vehicles by making their batteries available to electricity grids. We formulate a robust optimization problem that maximizes a vehicle owner’s expected profit from selling primary frequency regulation to the grid and guarantees that market commitments are met at all times for all frequency … Read more

    High-order Evaluation Complexity of a Stochastic Adaptive Regularization Algorithm for Nonconvex Optimization Using Inexact Function Evaluations and Randomly Perturbed Derivatives

  • Stefania Bellavia
  • Benedetta Morini
  • Philippe L. Toint
  • Gianmarco Gurioli
    • Categories Bound-constrained Optimization, Constrained Nonlinear Optimization, Unconstrained Optimization Tags , , ,

    A stochastic adaptive regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing strong approximate minimizers of any order for inexpensively constrained smooth optimization problems. For an objective function with Lipschitz continuous p-th derivative in a convex neighbourhood of the feasible set and given an arbitrary optimality order q, it … Read more

    On the use of Jordan Algebras for improving global convergence of an Augmented Lagrangian method in nonlinear semidefinite programming

  • Roberto Andreani
  • Ellen H. Fukuda
  • Gabriel Haeser
  • Daiana O. Santos
  • Leonardo D. Secchin
    • Categories Nonlinear Optimization, Semi-definite Programming Tags , , , ,

    Jordan Algebras are an important tool for dealing with semidefinite programming and optimization over symmetric cones in general. In this paper, a judicious use of Jordan Algebras in the context of sequential optimality conditions is done in order to generalize the global convergence theory of an Augmented Lagrangian method for nonlinear semidefinite programming. An approximate … Read more

    A derivative-free method for structured optimization problems

  • Andrea Cristofari
  • Francesco Rinaldi
    • Categories Nonlinear Optimization

    Structured optimization problems are ubiquitous in fields like data science and engineering. The goal in structured optimization is using a prescribed set of points, called atoms, to build up a solution that minimizes or maximizes a given function. In the present paper, we want to minimize a black-box function over the convex hull of a … Read more

    Solving Large-Scale Sparse PCA to Certifiable (Near) Optimality

  • Dimitris Bertsimas
  • Ryan Cory-Wright
  • Jean Pauphilet
    • Categories (Mixed) Integer Nonlinear Programming, Semi-definite Programming, Statistics Tags , , ,

    Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply certifiably optimal principal components with more than $p=100s$ of variables. By reformulating sparse PCA as a convex mixed-integer semidefinite optimization problem, we design a … Read more

    A tactical maintenance optimization model for multiple interconnected energy production systems

  • Silvia Anna Cordieri
  • Federico Malucelli
  • Ola Jabali
    • Categories (Mixed) Integer Linear Programming, Facility Planning and Design Tags , , , ,

    Multiple interconnected energy production systems are a common solution to satisfy the energy demand of industrial processes. Such energy demand is usually the combination of various energy types such as heat and electricity. This implies the installation of different technologies able to produce one or multiple energy types, to satisfy all energy needs. However, multiple … Read more

    Inexact and Stochastic Generalized Conditional Gradient with Augmented Lagrangian and Proximal Step

  • Jalal Fadili
  • Antonio Silveti-Falls
  • Cesare Molinari
    • Categories Convex and Nonsmooth Optimization, Semi-definite Programming, Stochastic Programming

    In this paper we propose and analyze inexact and stochastic versions of the CGALP algorithm developed in the authors’ previous paper, which we denote ICGALP, that allows for errors in the computation of several important quantities. In particular this allows one to compute some gradients, proximal terms, and/or linear minimization oracles in an inexact fashion … Read more

    Optimizing Diesel Fuel Supply Chain Operations for Hurricane Relief

  • Daniel Duque
  • David P. Morton
  • Haoxiang Yang
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , ,

    Hurricanes can cause severe property damage and casualties in coastal regions. Diesel fuel plays a crucial role in hurricane disaster relief. It is important to optimize fuel supply chain operations so that emergency demand for diesel can be mitigated in a timely manner. However, it can be challenging to estimate demand for fuel and make … Read more

    Decomposition Algorithms for Some Deterministic and Two-Stage Stochastic Single-Leader Multi-Follower Games

  • Pedro Borges de Melo
  • Claudia Sagastizábal
  • Mikhail V. Solodov
    • Categories Complementarity and Variational Inequalities, Nonsmooth Optimization, Stochastic Programming Tags , , , , ,

    We consider a certain class of hierarchical decision problems that can be viewed as single-leader multi-follower games, and be represented by a virtual market coordinator trying to set a price system for traded goods, according to some criterion that balances supply and demand. The objective function of the market coordinator involves the decisions of many … Read more

    A Primal–Dual Penalty Method via Rounded Weighted-\boldmath{$\ell_1$} Lagrangian Duality

  • Regina S. Burachik
  • Christopher J. Price
  • C. Yalcin Kaya
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization

    We propose a new duality scheme based on a sequence of smooth minorants of the weighted-$\ell_1$ penalty function, interpreted as a parametrized sequence of augmented Lagrangians, to solve nonconvex and nonsmooth constrained optimization problems. For the induced sequence of dual problems, we establish strong asymptotic duality properties. Namely, we show that (i) the sequence of … Read more