The convergence rate of the Sandwiching algorithm for convex bounded multiobjective optimization

  • Ina Lammel
  • Karl-Heinz Küfer
    • Categories Convex Optimization, Multi-Criteria Optimization Tags , , ,

    Sandwiching algorithms, also known as Benson-type algorithms, approximate the nondominated set of convex bounded multiobjective optimization problems by constructing and iteratively improving polyhedral inner and outer approximations. Using a set-valued metric, an estimate of the approximation quality is determined as the distance between the inner and outer approximation. The convergence of the algorithm is evaluated … Read more

    Submodular Dispatching with Multiple Vehicles

  • Ignacio Erazo
  • Alejandro Toriello
    • Categories Integer Programming, Production and Logistics, Transportation Tags , , , ,

    Motivated by applications in e-commerce logistics and production planning where orders (or items, or jobs) arrive at different times and must be dispatched or processed in batches, we consider a multi-vehicle dispatching problem that captures the tension between waiting for orders to arrive and the economies of scale due to batching. Our model extends the … Read more

    Singular value half thresholding algorithm for lp regularized matrix optimization problems

  • Peng Dingtao
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags , , , ,

    In this paper, we study the low-rank matrix optimization problem, where the penalty term is the $\ell_p~(0<p<1)$ regularization. Inspired by the good performance of half thresholding function in sparse/low-rank recovery problems, we propose a singular value half thresholding (SVHT) algorithm to solve the $\ell_p$ regularized matrix optimization problem. The main iteration in SVHT algorithm makes … Read more

    discrete location models with customers’ choice and path improvements

  • Inmaculada Espejo
  • Alfredo Marín
    • Categories (Mixed) Integer Linear Programming, Integer Programming Tags , , , , , ,

    We examine several facility location problems within a directed network involving two distinct cost types. The first, referred to as the customer cost, represents the expense each customer considers when selecting a facility to obtain service (e.g., delivery time or a measure of quality degradation). Consequently, once facilities are established, each customer chooses the one … Read more

    Accelerated Gradient Dynamics on Riemannian Manifolds: Faster Rate and Trajectory Convergence

  • Tejas Natu
  • Camille Castera
  • Jalal Fadili
  • Peter Ochs
    • Categories Convex Optimization, Optimization in Data Science Tags , , ,

    In order to minimize a differentiable geodesically convex function, we study a second-order dynamical system on Riemannian manifolds with an asymptotically vanishing damping term of the form \(\alpha/t\). For positive values of \(\alpha\), convergence rates for the objective values and convergence of trajectory is derived. We emphasize the crucial role of the curvature of the … Read more

    Near-optimal closed-loop method via Lyapunov damping for convex optimization

  • Camille Castera
  • Peter Ochs
    • Categories Convex Optimization, Systems governed by Differential Equations Optimization, Unconstrained Optimization Tags , , ,

    We introduce an autonomous system with closed-loop damping for first-order convex optimization. While, to this day, optimal rates of convergence are only achieved by non-autonomous methods via open-loop damping (e.g., Nesterov’s algorithm), we show that our system is the first one featuring a closed-loop damping while exhibiting a rate arbitrarily close to the optimal one. … Read more

    An outer approximation method for solving mixed-integer convex quadratic programs with indicators

  • Linchuan Wei
  • Simge Küçükyavuz
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming Tags , ,

    Mixed-integer convex quadratic programs with indicator variables (MIQP) encompass a wide range of applications, from statistical learning to energy, finance, and logistics. The outer approximation (OA) algorithm has been proven efficient in solving MIQP, and the key to the success of an OA algorithm is the strength of the cutting planes employed. In this paper, … Read more

    Distributionally robust optimization through the lens of submodularity

  • Karthik Natarajan
  • Divya Padmanabhan
  • Arjun Ramachandra
    • Categories Convex Optimization, Linear Programming, Linear, Cone and Semidefinite Programming Tags , , , ,

    Distributionally robust optimization is used to solve decision making problems under adversarial uncertainty where the distribution of the uncertainty is itself ambiguous. In this paper, we identify a class of these instances that is solvable in polynomial time by viewing it through the lens of submodularity. We show that the sharpest upper bound on the … Read more

    Robust Mask-Based Appointment Scheduling in Primary Care Practices

  • Sabrina Schmitz
  • Martin Comis
  • Christina Büsing
    • Categories Applications - OR and Management Sciences, Robust Optimization, Scheduling Tags , , ,

    In most health care systems, a primary care physician (PCP) is both the first instance consulted by patients with medical concerns and the instance coordinating patients’ continued access to medical care. Due to the PCP’s pivotal role, we address challenges of a high-quality primary care service by interday appointment scheduling on a tactical decision level. Our … Read more

    libDIPS — Discretization-Based Semi-Infinite and Bilevel Programming Solvers

  • Aron Zingler
  • Alexander Mitsos
  • Daniel Jungen
  • Hatim Djelassi
    • Categories Optimization Software and Modeling Systems, Robust Optimization, Semi-infinite Programming Tags , , , , ,

    We consider several hierarchical optimization programs: (generalized) semi-infinite and existence-constrained semi-infinite programs, minmax, and bilevel programs. Multiple adaptive discretization-based algorithms have been published for these program classes in recent decades. However, rigorous numerical performance comparisons between these algorithms are lacking. Indeed, if numerical comparisons are provided at all, they usually compare a small selection of … Read more