probabilistic programming

Machine Learning Algorithms for Assisting Solvers for Decision Optimization Problems

  • Morteza Kimiaei
  • Vyacheslav Kungurtsev
    • Categories Applications - OR and Management Sciences, Integer Programming, Optimization in Data Science Tags , , , , , , , ,

    Combinatorial decision problems lie at the intersection of Operations Research (OR) and Artificial Intelligence (AI), encompassing structured optimization tasks such as submodular selection, dynamic programming, planning, and scheduling. These problems exhibit exponential growth in decision complexity, driven by interdependent choices coupled through logical, temporal, and resource constraints.  Classical optimization frameworks—including integer programming, submodular optimization, and … Read more

    On mixed integer reformulations of monotonic probabilistic programming problems with discrete distributions

  • Vladimir I. Norkin
    • Categories (Mixed) Integer Nonlinear Programming, Finance and Economics, Stochastic Programming Tags , , , , ,

    The paper studies large scale mixed integer reformulation approach to stochastic programming problems containing probability and quantile functions, under assumption of discreteness of the probability distribution involved. Jointly with general sample approximation technique and contemporary mixed integer programming solvers the approach gives a regular framework to solution of practical probabilistic programming problems. In the literature … Read more

    A VaR Black-Litterman Model for the Construction of Absolute Return Fund-of-Funds

  • Miguel A. Lejeune
    • Categories Finance and Economics, Stochastic Programming Tags , , , , , ,

    The objective of this study is to construct fund-of-funds (FoF) that follow an absolute return strategy and meet the requirements imposed by the Value-at-Risk (VaR) market risk measure. We propose the VaR-Black Litterman model which accounts for the VaR and trading (diversification, buy-in threshold, liquidity, currency) requirements. The model takes the form of a probabilistic … Read more

    A Short Note on the Probabilistic Set Covering Problem

  • Anureet Saxena
    • Categories 0-1 Programming, Cutting Plane Approaches, Stochastic Programming Tags , , ,

    In this paper we address the following probabilistic version (PSC) of the set covering problem: min { cx | P (Ax>= xi) >= p, x_{j} in {0,1} j in N} where A is a 0-1 matrix, xi is a random 0-1 vector and p in (0,1] is the threshold probability level. In a recent development … Read more

    MIP Reformulations of the Probabilistic Set Covering Problem

  • Vineet Goyal
  • Miguel A. Lejeune
  • Anureet Saxena
    • Categories 0-1 Programming, Cutting Plane Approaches, Stochastic Programming Tags , , ,

    In this paper we address the following probabilistic version (PSC) of the set covering problem: $min \{ cx \ |\ {\mathbb P} (Ax\ge \xi) \ge p,\ x_{j}\in \{0,1\}^N\}$ where $A$ is a 0-1 matrix, $\xi$ is a random 0-1 vector and $p\in (0,1]$ is the threshold probability level. We formulate (PSC) as a mixed integer … Read more