Mechanical Engineering

Solving nonconvex SDP problems of structural optimization with stability control

  • Michal Kočvara
  • Michael Stingl
    • Categories Constrained Nonlinear Optimization, Mechanical Engineering, Semi-definite Programming Tags , , ,

    The goal of this paper is to formulate and solve structural optimization problems with constraints on the global stability of the structure. The stability constraint is based on the linear buckling phenomenon. We formulate the problem as a nonconvex semidefinite programming problem and introduce an algorithm based on the Augmented Lagrangian method combined with the … Read more

    On the modeling and control of delamination processes

  • Michal Kočvara
  • Jiri V. Outrata
    • Categories Constrained Nonlinear Optimization, Mechanical Engineering Tags , , ,

    This paper is motivated by problem of optimal shape design of laminated elastic bodies. We use a recently introduced model of delamination, based on minimization of potential energy which includes the free (Gibbs-type) energy and (pseudo)potential of dissipative forces, to introduce and analyze a special mathematical program with equilibrium constraints. The equilibrium is governed by … Read more

    Effective reformulations of the truss topology design problem

  • Michal Kočvara
  • Jiri V. Outrata
    • Categories Complementarity and Variational Inequalities, Mechanical Engineering, Nonlinear Optimization Tags ,

    We present a new formulation of the truss topology problem that results in unique design and unique displacements of the optimal truss. This is reached by adding an upper level to the original optimization problem and formulating the new problem as an MPCC (Mathematical Program with Complementarity Constraints). We derive optimality conditions for this problem … Read more

    PENNON – A Code for Convex Nonlinear and Semidefinite Programming

  • Michal Kočvara
  • Michael Stingl
    • Categories Convex Optimization, Mechanical Engineering, Semi-definite Programming

    We introduce a computer program PENNON for the solution of problems of convex Nonlinear and Semidefinite Programming (NLP-SDP). The algorithm used in PENNON is a generalized version of the Augmented Lagrangian method, originally introduced by Ben-Tal and Zibulevsky for convex NLP problems. We present generalization of this algorithm to convex NLP-SDP problems, as implemented in … Read more

    [PENNON – A Generalized Augmented Lagrangian Methodfor Semidefinite Programming

  • Michal Kočvara
  • Michael Stingl
    • Categories Mechanical Engineering, Second-Order Cone Programming, Semi-definite Programming

    This article describes a generalization of the PBM method by Ben-Tal and Zibulevsky to convex semidefinite programming problems. The algorithm used is a generalized version of the Augmented Lagrangian method. We present details of this algorithm as implemented in a new code PENNON. The code can also solve second-order conic programming (SOCP) problems, as well … Read more

    Mixed variable optimization of the number and composition of heat intercepts in a thermal insulation system

  • Charles Audet
  • John E. Dennis, Jr.
  • Michael Kokkolaras
    • Categories (Mixed) Integer Nonlinear Programming, Bound-constrained Optimization, Mechanical Engineering Tags , , , , ,

    In the literature, thermal insulation systems with a fixed number of heat intercepts have been optimized with respect to intercept locations and temperatures. The number of intercepts and the types of insulators that surround them were chosen by parametric studies. This was because the optimization methods used could not treat such categorical variables. Discrete optimization … Read more