Yuichi Takano

A Branch-and-Cut Algorithm for Solving Mixed-integer Semidefinite Optimization Problems

  • Ken Kobayashi
  • Yuichi Takano
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Semi-definite Programming Tags , , ,

    This paper is concerned with a cutting-plane algorithm for solving mixed-integer semidefinite optimization (MISDO) problems. In this algorithm, the positive semidefinite constraint is relaxed, and the resultant mixed-integer linear optimization problem is repeatedly solved with valid inequalities for the relaxed constraint. We prove convergence properties of the algorithm. Moreover, to speed up the computation, we … Read more

    Mixed Integer Quadratic Optimization Formulations for Eliminating Multicollinearity Based on Variance Inflation Factor

  • Ken Kobayashi
  • Tomomi Matsui
  • Ryuhei Miyashiro
  • Kazuhide Nakata
  • Yuichi Takano
  • Ryuta Tamura
    • Categories Applications - Science and Engineering, Integer Programming, Statistics Tags , , , , ,

    The variance inflation factor, VIF, is the most frequently used indicator for detecting multicollinearity in multiple linear regression models. This paper proposes two mixed integer quadratic optimization formulations for selecting the best subset of explanatory variables under upper-bound constraints on VIF of selected variables. Computational results illustrate the effectiveness of our optimization formulations based on … Read more

    Best subset selection for eliminating multicollinearity

  • Ken Kobayashi
  • Tomomi Matsui
  • Ryuhei Miyashiro
  • Kazuhide Nakata
  • Yuichi Takano
  • Ryuta Tamura
    • Categories Applications - Science and Engineering, Global Optimization, Integer Programming Tags , , , , ,

    This paper proposes a method for eliminating multicollinearity from linear regression models. Specifically, we select the best subset of explanatory variables subject to the upper bound on the condition number of the correlation matrix of selected variables. We first develop a cutting plane algorithm that, to approximate the condition number constraint, iteratively appends valid inequalities … Read more

    Bid Markup Decision and Resource Allocation for Cost Estimation in Competitive Bidding

  • Nobuaki Ishii
  • Yuichi Takano
  • Masaaki Muraki
    • Categories Applications - OR and Management Sciences Tags , , ,

    To receive a project contract through competitive bidding, contractors submit a bid price determined by putting a markup on the estimated project cost. Since a bid is inevitably affected by an inaccurate cost estimate, sufficient resources should be allocated to cost estimation. This paper develops a novel optimization model for determining the bid markup and … Read more

    Subset Selection by Mallows’ Cp: A Mixed Integer Programming Approach

  • Ryuhei Miyashiro
  • Yuichi Takano
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming, Statistics Tags , , ,

    This paper concerns a method of selecting the best subset of explanatory variables for a linear regression model. Employing Mallows’ C_p as a goodness-of-fit measure, we formulate the subset selection problem as a mixed integer quadratic programming problem. Computational results demonstrate that our method provides the best subset of variables in a few seconds when … Read more

    Mixed Integer Second-Order Cone Programming Formulations for Variable Selection

  • Ryuhei Miyashiro
  • Yuichi Takano
    • Categories (Mixed) Integer Nonlinear Programming, Second-Order Cone Programming, Statistics Tags , , , , ,

    This paper concerns the method of selecting the best subset of explanatory variables in a multiple linear regression model. To evaluate a subset regression model, some goodness-of-fit measures, e.g., adjusted R^2, AIC and BIC, are generally employed. Although variable selection is usually handled via a stepwise regression method, the method does not always provide the … Read more