Month: January 2019

Zeroth-order Nonconvex Stochastic Optimization: Handling Constraints, High-Dimensionality, and Saddle-Points

  • Krishnakumar Balasubramanian
  • Saeed Ghadimi
    • Categories Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on addressing constrained optimization, high-dimensional setting, and saddle-point avoiding. To handle constrained optimization, we first propose generalizations of the conditional gradient algorithm achieving rates similar to the standard stochastic gradient algorithm using only zeroth-order information. To … Read more

    Bin Packing Problem with Time Dimension: An Application in Cloud Computing

  • Nursen Aydin
  • Ş. İlker Birbil
  • Ibrahim Muter
    • Categories Applications - OR and Management Sciences Tags , , , ,

    Improving energy efficiency and lowering operational costs are the main challenges faced in systems with multiple servers. One prevalent objective in such systems is to minimize the number of servers required to process a given set of tasks under server capacity constraints. This objective leads to the well-known bin packing problem. In this study, we … Read more

    Best Subset Selection via Cross-validation Criterion

  • Ryuhei Miyashiro
  • Yuichi Takano
    • Categories Integer Programming, Statistics Tags , , , ,

    This paper is concerned with the cross-validation criterion for best subset selection in a linear regression model. In contrast with the use of statistical criteria (e.g., Mallows’ $C_p$, AIC, BIC, and various information criteria), the cross-validation only requires the mild assumptions, namely, samples are identically distributed, and training and validation samples are independent. For this … Read more

    A fully mixed-integer linear programming formulation for economic dispatch with valve-point effects, transmission loss and prohibited operating zones

  • Huangyue Chen
  • Jinbao Jian
  • Shanshan Pan
  • Linfeng Yang
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering Tags , , , , ,

    Economic dispatch (ED) problem considering valve-point effects (VPE), transmission loss and prohibited operating zones (POZ) is a very challenging issue due to its intrinsic non-convex, non-smooth and non-continuous natures. To achieve a near globally solution, a fully mixed-integer linear programming (FMILP) formulation is proposed for such an ED problem. Since the original loss function is … Read more

    Two-stage Stochastic Programming with Linearly Bi-parameterized Quadratic Recourse

  • Ying Cui
  • Junyi Liu
  • Jong-Shi Pang
  • Suvrajeet Sen
    • Categories Stochastic Programming Tags , ,

    This paper studies the class of two-stage stochastic programs (SP) with a linearly bi-parameterized recourse function defined by a convex quadratic program. A distinguishing feature of this new class of stochastic programs is that the objective function in the second stage is linearly parameterized by the first-stage decision variable, in addition to the standard linear … Read more

    Coupled task scheduling with time-dependent processing times

  • Mostafa Khatami
  • Amir Salehipour
    • Categories Applications - OR and Management Sciences, Scheduling

    The single machine coupled task scheduling problem includes a set of jobs, each with two separated tasks and there is an exact delay between the tasks. We investigate the single machine coupled task scheduling problem with the objective of minimizing the makespan under identical processing time for the first task and identical delay period for … Read more

    Forecasting conceivable interest rate market scenarios and significant losses on interest rate portfolios using mathematical optimization

  • Katsuhiro Tanaka
    • Categories Constrained Nonlinear Optimization, Finance and Economics Tags , , , , ,

    This study proposes a mathematical optimization programming model that simultaneously forecasts interest rate market scenarios and significant losses on interest rate market portfolios. The model includes three main components. A constraint condition is set using the Mahalanobis distance, which consists of innovation terms in a dynamic conditional correlation-generalized autoregressive conditional heteroscedasticity (DCC-GARCH) model that represent … Read more

    Coupled task scheduling with exact delays: Literature review and models

  • T.C.E. Cheng
  • Mostafa Khatami
  • Amir Salehipour
    • Categories Applications - OR and Management Sciences, Scheduling

    The coupled task scheduling problem concerns scheduling a set of jobs, each with at least two tasks and there is an exact delay period between two consecutive tasks, on a set of machines to optimize a performance criterion. While research on the problem dates back to the 1980s, interests in the computational complexity of variants … Read more

    Approximating L1-Norm Best-Fit Lines

  • J. Paul Brooks
  • JH Dulá
    • Categories Data-Mining

    Sufficient conditions are provided for a deterministic algorithm for estimating an L1-norm best-fit one-dimensional subspace. To prove the conditions are sufficient, fundamental properties of the L1-norm projection of a point onto a one-dimensional subspace are derived. Also, an equivalence is established between the algorithm, which involves the calculation of several weighted medians, and independently-derived algorithms … Read more

    Algorithms for single- and multiple-runway Aircraft Landing Problem

  • Amir Salehipour
    • Categories Applications - OR and Management Sciences, Scheduling

    The Aircraft Landing Problem is the problem of allocating an airport’s runways to arriving aircraft as well as scheduling the landing time of aircraft, with the objective of minimizing total deviations from the target landing times. This work proposes new approaches to solve the Aircraft Landing Problem. The distinguishing factors of the proposed approaches include … Read more