Nonlinear Model Predictive Control via Feasibility-Perturbed Sequential Quadratic Programming

  • J B Rawlings
  • M. J. Tenny
  • Stephen Wright
    • Categories Chemical Engineering, Constrained Nonlinear Optimization, Control Applications Tags , ,

    Model predictive control requires the solution of a sequence of continuous optimization problems that are nonlinear if a nonlinear model is used for the plant. We describe briefly a trust-region feasibility-perturbed sequential quadratic programming algorithm (developed in a companion report), then discuss its adaptation to the problems arising in nonlinear model predictive control. Computational experience … Read more

    A Simplified/Improved HKM Direction for Certain Classes of Semidefinite Programming

  • Franz Rendl
  • Renata Sotirov
  • Henry Wolkowicz
    • Categories Constrained Nonlinear Optimization, Semi-definite Programming Tags , , ,

    Semidefinite Programming (SDP) provides strong bounds for many NP-hard combinatorial problems. Arguably the most popular/efficient search direction for solving SDPs using a primal-dual interior point (p-d i-p) framework is the {\em HKM direction}. This direction is a Newton direction found from the linearization of a symmetrized version of the optimality conditions. For many of the … Read more

    Implementation of Interior Point Methods for Mixed Semidefinite and Second Order Cone Optimization Problems

  • Jos F. Sturm
    • Categories Linear, Cone and Semidefinite Programming Tags , , , ,

    There is a large number of implementational choices to be made for the primal-dual interior point method in the context of mixed semidefinite and second order cone optimization. This paper presents such implementational issues in a unified framework, and compares the choices made by different research groups. This is also the first paper to provide … Read more

    Solving second order cone programming via a reduced augmented system approach

  • Zhi Cai
  • Kim-Chuan Toh
    • Categories Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems Tags , , ,

    The standard Schur complement equation based implementation of interior-point methods for second order cone programming may encounter stability problems in the computation of search directions, and as a consequence, accurate approximate optimal solutions are sometimes not attainable. Based on the eigenvalue decomposition of the $(1,1)$ block of the augmented equation, a reduced augmented equation approach … Read more

    Computation of Minimum Volume Covering Ellipsoids

  • Robert M. Freund
  • Peng Sun
    • Categories Applications - OR and Management Sciences, Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    We present a practical algorithm for computing the minimum volume n-dimensional ellipsoid that must contain m given points a_1, …, a_m \in R^n. This convex constrained problem arises in a variety of applied computational settings, particularly in data mining and robust statistics. Its structure makes it particularly amenable to solution by interior-point methods, and it … Read more

    Unifying Condition Numbers for Linear Programming

  • Dennis Cheung
  • Javier F. Peña
  • Felipe Cucker
    • Categories Linear Programming Tags , ,

    In recent years, several condition numbers were defined for a variety of linear programming problems based upon relative distances to ill-posedness. In this paper we provide a unifying view of these condition numbers. To do so, we introduce yet another linear programming problem and show that its distance to ill-posedness naturally captures the most commonly … Read more

    Distance Weighted Discrimination

  • J. S. Marron
  • Michael J. Todd
    • Categories Second-Order Cone Programming, Statistics Tags ,

    High Dimension Low Sample Size statistical analysis is becoming increasingly important in a wide range of applied contexts. In such situations, it is seen that the popular Support Vector Machine suffers from “data piling” at the margin, which can diminish generalizability. This leads naturally to the development of Distance Weighted Discrimination, which is based on … Read more

    Interior-Point Methods for Nonconvex Nonlinear Programming: Complementarity Constraints

  • Hande Benson
  • David F. Shanno
  • Robert J. Vanderbei
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , ,

    In this paper, we present the formulation and solution of optimization problems with complementarity constraints using an interior-point method for nonconvex nonlinear programming. We identify possible difficulties that could arise, such as unbounded faces of dual variables, linear dependence of constraint gradients and initialization issues. We suggest remedies. We include encouraging numerical results on the … Read more

    A Class of Hybrid Methods for Revenue Management

  • William Cooper
  • Tito Homem-de-Mello
    • Categories Dynamic Programming, Stochastic Programming, Yield Management

    We consider a Markov decision process model of a network revenue management problem. Working within this formal framework, we study policies that combine aspects of mathematical programming approaches and pure Markov decision process methods. The policies employ heuristics early in the booking horizon, and switch to a more-detailed decision rule closer to the time of … Read more

    TfMin: Short Reference Manual

  • Jean-Baptiste Caillau
  • Joseph Noailles
  • Joseph Gergaud
    • Categories Control Applications Tags , , ,

    This is a short guide to use the Fortran and Matlab package TfMin designed for the numerical solution of continuous 3D minimum-time orbit transfer around the Earth (with free final longitude), especially for low thrust engines. The underlying method is single shooting. The Matlab interface with the solver allows the user to define the problem … Read more