Policy with guaranteed risk-adjusted performance for multistage stochastic linear problems

  • Bernardo Freitas Paulo da Costa
  • Vincent Leclère
    • Categories Convex Optimization, Dynamic Programming, Stochastic Programming Tags , , ,

    Risk-averse multi-stage problems and their applications are gaining interest in various fields of applications. Under convexity assumptions, the resolution of these problems can be done with trajectory following dynamic programming algorithms like Stochastic Dual Dynamic Programming (SDDP) to access a deterministic lower bound, and dual SDDP for deterministic upper bounds. In this paper, we leverage … Read more

    Optimization Over Trained Neural Networks: Taking a Relaxing Walk

  • Jiatai Tong
  • Junyang Cai
  • Thiago Serra
    • Categories (Mixed) Integer Linear Programming, Data-Mining, Meta Heuristics

    Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However, solving these formulations soon becomes difficult as the network size grows due to the weak linear relaxation and dense constraint matrix. We have seen … Read more

    Sparse Polynomial Optimization with Unbounded Sets

  • Jie Wang
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Semi-definite Programming Tags , , , ,

    This paper considers sparse polynomial optimization with unbounded sets. When the problem possesses correlative sparsity, we propose a sparse homogenized Moment-SOS hierarchy with perturbations to solve it. The new hierarchy introduces one extra auxiliary variable for each variable clique according to the correlative sparsity pattern. Under the running intersection property, we prove that this hierarchy … Read more

    Active Set-based Inexact Proximal Bundle Algorithm for Stochastic Quadratic Programming

  • Niloofar Fadavi
  • Harsha Gangammanavar
    • Categories Convex Optimization, Stochastic Programming Tags , , , ,

    In this paper, we examine two-stage stochastic quadratic programming problems, where the objective function of the first and second stages are quadratic functions, and the constraints are linear. The uncertainty is associated with the second-stage right-hand side and variable bounds. In large-scale settings, when the number of scenarios necessary to represent the underlying stochastic process … Read more

    Tactical workforce sizing and scheduling decisions for last-mile delivery

  • Alberto Santini
  • Claudia Archetti
    • Categories (Mixed) Integer Linear Programming, Production and Logistics, Scheduling Tags , , ,

    We tackle the problems of workforce sizing and shift scheduling of a logistic operator delivering parcels in the last-mile segment of the supply chain. Our working hypothesis is that the relevant decisions are affected by two main trade-offs: workforce size and shift stability. A large workforce is able to deal with demand fluctuations but incurs … Read more

    A low-rank augmented Lagrangian method for large-scale semidefinite programming based on a hybrid convex-nonconvex approach

  • Renato D.C. Monteiro
  • Arnesh Sujanani
  • Diego Cifuentes
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , , , , ,

    This paper introduces HALLaR, a new first-order method for solving large-scale semidefinite programs (SDPs) with bounded domain. HALLaR is an inexact augmented Lagrangian (AL) method where the AL subproblems are solved by a novel hybrid low-rank (HLR) method. The recipe behind HLR is based on two key ingredients: 1) an adaptive inexact proximal point method … Read more

    Post-Processing with Projection and Rescaling Algorithms for Semidefinite Programming

  • Shin-ichi Kanoh
  • Akiko Yoshise
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming, Semi-definite Programming

    We propose the algorithm that solves the symmetric cone programs (SCPs) by iteratively calling the projection and rescaling methods the algorithms for solving exceptional cases of SCP. Although our algorithm can solve SCPs by itself, we propose it intending to use it as a post-processing step for interior point methods since it can solve the … Read more

    Solving moment and polynomial optimization problems on Sobolev spaces

  • Didier Henrion
  • Alessandro Rudi
    • Categories Global Optimization, Infinite Dimensional Optimization, Semi-definite Programming Tags , , ,

    Using standard tools of harmonic analysis, we state and solve the problem of moments for positive measures supported on the unit ball of a Sobolev space of multivariate periodic trigonometric functions. We describe outer and inner semidefinite approximations of the cone of Sobolev moments. They are the basic components of an infinite-dimensional moment-sums of squares … Read more

    Design Guidelines for Noise-Tolerant Optimization with Applications in Robust Design

  • Yuchen Lou
  • Shigeng Sun
  • Jorge Nocedal
    • Categories Nonlinear Optimization, Optimization of Systems modeled by PDEs, Stochastic Programming

    The development of nonlinear optimization algorithms capable of performing reliably in the presence of noise has garnered considerable attention lately. This paper advocates for strategies to create noise-tolerant nonlinear optimization algorithms by adapting classical deterministic methods. These adaptations follow certain design guidelines described here, which make use of estimates of the noise level in the … Read more

    Using generalized simplex methods to approximate derivatives

  • Gabriel Jarry-Bolduc
    • Categories Nonlinear Optimization Tags , ,

    This paper presents two methods for approximating a proper subset of the entries of a Hessian using only function evaluations. These approximations are obtained using the techniques called generalized simplex Hessian and generalized centered simplex Hessian. We show how to choose the matrices of directions involved in the computation of these two techniques depending on … Read more