mixed-integer convex programming

On Tractability, Complexity, and Mixed-Integer Convex Programming Representability of Distributionally Favorable Optimization

  • Nan Jiang
  • Weijun Xie
    • Categories Stochastic Programming Tags , ,

    Distributionally Favorable Optimization (DFO) is an important framework for decision-making under uncertainty, with applications across fields such as reinforcement learning, online learning, robust statistics, chance-constrained programming, and two-stage stochastic optimization without relatively complete recourse. In contrast to the traditional Distributionally Robust Optimization (DRO) paradigm, DFO presents a unique challenge– the application of the inner infimum … Read more

    Solving Multiobjective Mixed Integer Convex Optimization Problems

  • Marianna De Santis
  • Gabriele Eichfelder
  • Julia Niebling
  • Stefan Rocktäschel
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Multi-Criteria Optimization Tags , ,

    Multiobjective mixed integer convex optimization refers to mathematical programming problems where more than one convex objective function needs to be optimized simultaneously and some of the variables are constrained to take integer values. We present a branch-and-bound method based on the use of properly defined lower bounds. We do not simply rely on convex relaxations, … Read more

    A new combinatorial algorithm for separable convex resource allocation with nested bound constraints

  • Qie He
  • Kameng Nip
  • Zeyang Wu
    • Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization Tags , , ,

    The separable convex resource allocation problem with nested bound constraints aims to allocate $B$ units of resources to $n$ activities to minimize a separable convex cost function, with lower and upper bounds on the total amount of resources that can be consumed by nested subsets of activities. We develop a new combinatorial algorithm to solve … Read more

    A disjunctive convex programming approach to the pollution routing problem

  • Ricardo Fukasawa
  • Qie He
  • Yongjia Song
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Transportation Tags , , ,

    The pollution routing problem (PRP) aims to determine a set of routes and speed over each leg of the routes simultaneously to minimize the total operational and environmental costs. A common approach to solve the PRP exactly is through speed discretization, i.e., assuming that speed over each arc is chosen from a prescribed set of … Read more

    Exact and Heuristic Approaches for Directional Sensor Control

  • Hans D Mittelmann
  • Domenico Salvagnin
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Control Applications Tags , , ,

    Directional sensors are gaining importance due to applications, in- cluding surveillance, detection, and tracking. Such sensors have a limited fi eld-of-view and a discrete set of directions they can be pointed to. The Directional Sensor Control problem (DSCP) consists in assigning a direction of view to each sensor. The location of the targets is known with … Read more

    Closedness of Integer Hulls of Simple Conic Sets

  • Santanu S. Dey
  • Diego Moran Ramirez
    • Categories (Mixed) Integer Nonlinear Programming Tags , ,

    Let $C$ be a full-dimensional pointed closed convex cone in $R^m$ obtained by taking the conic hull of a strictly convex set. Given $A \in Q^{m \times n_1}$, $B \in Q^{m \times n_2}$ and $b \in Q^m$, a simple conic mixed-integer set (SCMIS) is a set of the form $\{(x,y)\in Z^{n_1} \times R^{n_2}\,|\,\ Ax +By … Read more