warm-start

Missing Value Imputation via Mathematical Optimization with Instance-and-Feature Neighborhoods

  • Yuichi Takano
    • Categories (Mixed) Integer Nonlinear Programming, Optimization in Data Science Tags , , , ,

    Datasets collected for analysis often contain a certain amount of incomplete instances, where some feature values are missing. Since many statistical analyses and machine learning algorithms depend on complete datasets, missing values need to be imputed in advance. Bertsimas et al. (2018) proposed a high-performance method that combines machine learning and mathematical optimization algorithms for … Read more

    Solving Heated Oil Pipeline Problems Via Mixed Integer Nonlinear Programming Approach

  • Yu-Hong Dai
  • Yakui Huang
  • Bo Li
  • Muming Yang
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences Tags , , , , , ,

    It is a crucial problem how to heat oil and save running cost for crude oil transport. This paper strictly formulates such a heated oil pipeline problem as a mixed integer nonlinear programming model. Nonconvex and convex continuous relaxations of the model are proposed, which are proved to be equivalent under some suitable conditions. Meanwhile, … Read more

    Warm-start of interior point methods for second order cone optimization via rounding over optimal Jordan frames

  • Sertalp B. Çay
  • Imre Pólik
  • Tamás Terlaky
    • Categories Branch and Cut Algorithms, Second-Order Cone Programming Tags , , , ,

    Interior point methods (IPM) are the most popular approaches to solve Second Order Cone Optimization (SOCO) problems, due to their theoretical polynomial complexity and practical performance. In this paper, we present a warm-start method for primal-dual IPMs to reduce the number of IPM steps needed to solve SOCO problems that appear in a Branch and … Read more

    New Analysis and Results for the Conditional Gradient Method

  • Robert M. Freund
  • Paul Grigas
    • Categories Convex Optimization Tags , , , ,

    We present new results for the conditional gradient method (also known as the Frank-Wolfe method). We derive computational guarantees for arbitrary step-size sequences, which are then applied to various step-size rules, including simple averaging and constant step-sizes. We also develop step-size rules and computational guarantees that depend naturally on the warm-start quality of the initial … Read more

    Constraint Reduction with Exact Penalization for Model-Predictive Rotorcraft Control

  • Aaron L. Greenfield
  • Meiyun Y. He
  • Vineet Sahasrabudhe
  • André L. Tits
    • Categories Applications - Science and Engineering, Control Applications, Quadratic Programming Tags , , , , , , , , ,

    Model Predictive Control (also known as Receding Horizon Control (RHC)) has been highly successful in process control applications. Its use for aerospace applications has been hindered by its high computational requirements. In the present paper, we propose using enhanced primal-dual interior-point optimization techniques in the convex-quadratic-program-based RHC control of a rotorcraft. Our enhancements include a … Read more

    An Adaptive Primal-Dual Warm-Start Technique for Quadratic Multiobjective Optimization

  • Jörg Fliege
    • Categories Control Applications, Multi-Criteria Optimization, Quadratic Programming Tags , , ,

    We present a new primal-dual algorithm for convex quadratic multicriteria optimization. The algorithm is able to adaptively refine the approximation to the set of efficient points by way of a warm-start interior-point scalarization approach. Results of this algorithm when applied on a three-criteria real-world power plant optimization problem are reported, thereby illustrating the feasibility of … Read more

    A Warm-Start Approach for Large-Scale Stochastic Linear Programs

  • Marco Colombo
  • Jacek Gondzio
  • Andreas Grothey
    • Categories Linear Programming, Stochastic Programming Tags , ,

    We describe a method of generating a warm-start point for interior point methods in the context of stochastic programming. Our approach exploits the structural information of the stochastic problem so that it can be seen as a structure-exploiting initial point generator. We solve a small-scale version of the problem corresponding to a reduced event tree … Read more

    On warm starts for interior methods

  • Anders Forsgren
    • Categories Constrained Nonlinear Optimization Tags , , ,

    An appealing feature of interior methods for linear programming is that the number of iterations required to solve a problem tends to be relatively insensitive to the choice of initial point. This feature has the drawback that it is difficult to design interior methods that efficiently utilize information from an optimal solution to a “nearby” … Read more

    An Algorithm for Perturbed Second-order Cone Programs

  • Yu Xia
    • Categories Complementarity and Variational Inequalities, Nonsmooth Optimization, Second-Order Cone Programming Tags , , ,

    The second-order cone programming problem is reformulated into several new systems of nonlinear equations. Assume the perturbation of the data is in a certain neighborhood of zero. Then starting from a solution to the old problem, the semismooth Newton’s iterates converge Q-quadratically to a solution of the perturbed problem. The algorithm is globalized. Numerical examples … Read more

    An Efficient Interior-Point Method for Convex Multicriteria Optimization Problems

  • Jörg Fliege
    • Categories Convex Optimization, Multi-Criteria Optimization Tags , , , ,

    In multicriteria optimization, several objective functions, conflicting with each other, have to be minimized simultaneously. We propose a new efficient method for approximating the solution set of a multiobjective programming problem, where the objective functions involved are arbitary convex functions and the set of feasible points is convex. The method is based on generating warm-start … Read more