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3869 results in Optimization

Page 32 of 194

  • ANZ VOLUME 62 ISSUE 4 COVER AND FRONT MATTER

  • Journal:
    The ANZIAM Journal / Volume 62 / Issue 4 / October 2020
    Published online by Cambridge University Press:
    20 April 2021, pp. f1-f2
    • Article
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  • EDITORIAL: SPECIAL ISSUE CELEBRATING THE ACHIEVEMENTS OF PROFESSOR G. C. WAKE

  • MARK I. NELSON, RODNEY O. WEBER
  • Journal:
    The ANZIAM Journal / Volume 62 / Issue 4 / October 2020
    Published online by Cambridge University Press:
    20 April 2021, pp. 353-354
    • Article
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  • ANZ VOLUME 62 ISSUE 4 COVER AND BACK MATTER

  • Journal:
    The ANZIAM Journal / Volume 62 / Issue 4 / October 2020
    Published online by Cambridge University Press:
    20 April 2021, pp. b1-b5
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  • STOCHASTIC MODEL PREDICTIVE CONTROL FOR SPACECRAFT RENDEZVOUS AND DOCKING VIA A DISTRIBUTIONALLY ROBUST OPTIMIZATION APPROACH

  • Part of
  • ZUOXUN LI, KAI ZHANG
  • Journal:
    The ANZIAM Journal / Volume 63 / Issue 1 / January 2021
    Published online by Cambridge University Press:
    19 April 2021, pp. 39-57

  • A stochastic model predictive control (SMPC) algorithm is developed to solve the problem of three-dimensional spacecraft rendezvous and docking with unbounded disturbance. In particular, we only assume that the mean and variance information of the disturbance is available. In other words, the probability density function of the disturbance distribution is not fully known. Obstacle avoidance is considered during the rendezvous phase. Line-of-sight cone, attitude control bandwidth, and thrust direction constraints are considered during the docking phase. A distributionally robust optimization based algorithm is then proposed by reformulating the SMPC problem into a convex optimization problem. Numerical examples show that the proposed method improves the existing model predictive control based strategy and the robust model predictive control based strategy in the presence of disturbance.

  • 6 - Mixed-Integer Programming Models

  • Ignacio E. Grossmann, Carnegie Mellon University, Pennsylvania
  • Book:
    Advanced Optimization for Process Systems Engineering
    Published online:
    11 June 2021
    Print publication:
    25 March 2021, pp 53-61

  • Summary

    This chapter introduces basic models for mixed-integer linear programming. It starts with multiple-choice constraints, and implications that are formulated as inequalities with 0-1 variables. Next, constraints with continuous variables are introduced, such as discontinuous domains and cost functions with fixed charges, which are formulated as linear mixed-integer constraints. Finally, the chapter closes by introducing classic OR problems, the assignment problem, facility location problem, knapsack problem, set covering problem and the traveling salesman problem, all of which are formulated as linear integer and mixed-integer linear programming models.

  • 13 - Lagrangean Decomposition

  • Ignacio E. Grossmann, Carnegie Mellon University, Pennsylvania
  • Book:
    Advanced Optimization for Process Systems Engineering
    Published online:
    11 June 2021
    Print publication:
    25 March 2021, pp 119-128

  • Summary

    This chapter addresses the decomposition of MILP optimization problems that involve complicating constraints. It is shown that, by dualizing the complicating constraints, one can derive the Lagrangean relaxation that yields a lower bound to the optimal solution. It is also shown that, by duplicating variables, one can dualize the corresponding equalities yielding the Lagrangean decomposition method that can predict stronger lower bounds than the Lagrangean relaxationn. The steps involved in this decomposition method are described, and can be exended to NLP and MINLP problems.

  • 3 - Basic Theoretical Concepts in Optimization

  • Ignacio E. Grossmann, Carnegie Mellon University, Pennsylvania
  • Book:
    Advanced Optimization for Process Systems Engineering
    Published online:
    11 June 2021
    Print publication:
    25 March 2021, pp 16-31

  • Summary

    This chapter first introduces basic concepts in nonlinear optimization, especially feasible regions and convexity conditions. Sufficient conditions are provided for both convex regions and convex functions. Next, optimality conditions are presented for unconstrained optimization problems (stationary conditions), and constrained problems with equality constraints (stationary condition of Lagrange function) and with inequality constraints (Fritz-John Theorem).The chapter concludes with nonlinear optimization with equality and equalityconstraints that lead to the Karush–Kuhn–Tucker conditions. Finally, an active set strategy is introduced for the solution of small nonlinear programming problems, and is illustrated with a small example.

Page 32 of 194