Power-Capacity and Ramp-Capability Reserves for Wind Integration in Power-Based UC

  • Ross Baldick
  • Germán Morales-España
  • Javier García-González
  • Andres Ramos
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , , ,

    This paper proposes a power-based network-constrained unit commitment (UC) model as an alternative to the traditional deterministic UCs to deal with wind generation uncertainty. The formulation draws a clear distinction between power-capacity and ramp-capability reserves to deal with wind production uncertainty. These power and ramp requirements can be obtained from wind forecast information. The model … Read more

    A Tight MIP Formulation of the Unit Commitment Problem with Start-up and Shut-down Constraints

  • Claudio Gentile
  • Germán Morales-España
  • Andres Ramos
    • Categories (Mixed) Integer Linear Programming, Scheduling Tags , ,

    This paper provides the convex hull description for the following basic operating constraints of a single power generation unit in Unit Commitment (UC) problems: 1) generation limits, 2) startup and shutdown capabilities, and 3) minimum up and down times. Although the model does not consider some crucial constraints, such as ramping, the proposed constraints can … Read more

    Tight MIP Formulations of the Power-Based Unit Commitment Problem

  • Claudio Gentile
  • Germán Morales-España
  • Andres Ramos
    • Categories (Mixed) Integer Linear Programming, Scheduling Tags , , , , ,

    This paper provides the convex hull description for the basic operation of slow- and quick-start units in power-based unit commitment (UC) problems. The basic operating constraints that are modeled for both types of units are: 1) generation limits and 2) minimum up and down times. Apart from this, the startup and shutdown processes are also … Read more

    Stochastic Topology Design Optimization for Continuous Elastic Materials

  • Miguel Carrasco
  • Benjamin Ivorra
  • Ángel M. Ramos
    • Categories Mechanical Engineering, Multidisciplinary Design Optimization, Stochastic Programming

    In this paper, we develop a stochastic model for topology optimization. We find robust structures that minimize the compliance for a given main load having a stochastic behavior. We propose a model that takes into account the expected value of the compliance and its variance. We show that, similarly to the case of truss structures, … Read more

    Analyzing Node-Weighted Oblivious Matching Problem via Continuous LP with Jump Discontinuity

  • T-H. Hubert Chan
  • Fei Chen
  • Xiaowei Wu
    • Categories Graphs and Matroids Tags , ,

    We prove the first non-trivial performance ratio strictly above 0.5 for the weighted Ranking algorithm on the oblivious matching problem where nodes in a general graph can have arbitrary weights. We have discovered a new structural property of the ranking algorithm: if a node has two unmatched neighbors, then it will still be matched even … Read more

    An Accelerated Proximal Coordinate Gradient Method and its Application to Regularized Empirical Risk Minimization

  • Qihang Lin
  • Zhaosong Lu
  • Lin Xiao
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization, Stochastic Programming Tags , ,

    We consider the problem of minimizing the sum of two convex functions: one is smooth and given by a gradient oracle, and the other is separable over blocks of coordinates and has a simple known structure over each block. We develop an accelerated randomized proximal coordinate gradient (APCG) method for minimizing such convex composite functions. … Read more

    Linear conic optimization for nonlinear optimal control

  • Didier Henrion
  • Edouard Pauwels
    • Categories Control Applications, Infinite Dimensional Optimization, Semi-definite Programming

    Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual linear problem consists of finding the largest lower bound on the value function of the optimal control problem. Various approximation results relating the original optimal control … Read more

    An Augmented Lagrangian based Algorithm for Distributed Non-Convex Optimization

  • Moritz Diehl
  • Janick V Frasch
  • Boris Houska
    • Categories Constrained Nonlinear Optimization Tags , ,

    This paper is about distributed derivative-based algorithms for solving optimization problems with a separable (potentially nonconvex) objective function and coupled affine constraints. A parallelizable method is proposed that combines ideas from the fields of sequential quadratic programming and augmented Lagrangian algorithms. The method negotiates shared dual variables that may be interpreted as prices, a concept … Read more

    On Global Optimization

  • Isaac Siwale
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Multi-Criteria Optimization Tags , , , ,

    This paper presents a relatively “unfettered” method for finding global optima to constrained nonlinear programs. The method reformulates the given program into a bi-objective mixed-integer program that is then solved for the Nash equilibrium. A numerical example (whose solution provides a new benchmark against which other algorithms may be assessed) is included to illustrate the … Read more

    Constraint aggregation for rigorous global optimization

  • Ferenc Domes
  • Arnold Neumaier
    • Categories Global Optimization Tags , , , , ,

    In rigorous constrained global optimization, upper bounds on the objective function help to reduce the search space. Their construction requires finding a narrow box around an approximately feasible solution, verified to contain a feasible point. Approximations are easily found by local optimization, but the verification often fails. In this paper we show that even if … Read more