Selvaprabu Nadarajah

A Data Efficient and Feasible Level Set Method for Stochastic Convex Optimization with Expectation Constraints

  • Qihang Lin
  • Selvaprabu Nadarajah
  • Negar Soheili
  • Tianbao Yang
    • Categories Convex Optimization, Stochastic Programming Tags , , ,

    Stochastic convex optimization problems with expectation constraints (SOECs) are encountered in statistics and machine learning, business, and engineering. In data-rich environments, the SOEC objective and constraints contain expectations defined with respect to large datasets. Therefore, efficient algorithms for solving such SOECs need to limit the fraction of data points that they use, which we refer … Read more

    Network-based Approximate Linear Programming for Discrete Optimization

  • Andre Augusto Cire
  • Selvaprabu Nadarajah
    • Categories (Mixed) Integer Nonlinear Programming, Dynamic Programming, Linear Programming Tags , ,

    We develop a new class of approximate linear programs (ALPs) that project the high-dimensional value function of dynamic programs onto a class of basis functions, each defined as a network that represents aggregrations over the state space. The resulting ALP is a minimum-cost flow problem over an extended variable space that synchronizes flows across multiple … Read more

    A Level-set Method For Convex Optimization with a Feasible Solution Path

  • Qihang Lin
  • Selvaprabu Nadarajah
  • Negar Soheili
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    Large-scale constrained convex optimization problems arise in several application domains. First-order methods are good candidates to tackle such problems due to their low iteration complexity and memory requirement. The level-set framework extends the applicability of first-order methods to tackle problems with complicated convex objectives and constraint sets. Current methods based on this framework either rely … Read more

    Revisiting Approximate Linear Programming Using a Saddle Point Approach

  • Qihang Lin
  • Selvaprabu Nadarajah
  • Negar Soheili
    • Categories Dynamic Programming, Semi-infinite Programming, Stochastic Programming Tags , , , , ,

    Approximate linear programs (ALPs) are well-known models for computing value function approximations (VFAs) of intractable Markov decision processes (MDPs) arising in applications. VFAs from ALPs have desirable theoretical properties, define an operating policy, and provide a lower bound on the optimal policy cost, which can be used to assess the suboptimality of heuristic policies. However, … Read more

    Partial hyperplane activation for generalized intersection cuts

  • Egon Balas
  • Aleksandr M. Kazachkov
  • François Margot
  • Selvaprabu Nadarajah
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags , ,

    The generalized intersection cut (GIC) paradigm is a recent framework for generating cutting planes in mixed integer programming with attractive theoretical properties. We investigate this computationally unexplored paradigm and observe that a key hyperplane activation procedure embedded in it is not computationally viable. To overcome this issue, we develop a novel replacement to this procedure … Read more