stochastic optimization

On the Trade-Off Between Distributional Belief and Ambiguity: Conservatism, Finite-Sample Guarantees, and Asymptotic Properties

  • Man Yiu Tsang
  • Karmel S. Shehadeh
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    We propose and analyze a new data-driven trade-off (TRO) approach for modeling uncertainty that serves as a middle ground between the optimistic approach, which adopts a distributional belief, and the pessimistic distributionally robust optimization approach, which hedges against distributional ambiguity. We equip the TRO model with a TRO ambiguity set characterized by a size parameter … Read more

    Modified Line Search Sequential Quadratic Methods for Equality-Constrained Optimization with Unified Global and Local Convergence Guarantees

  • Albert S. Berahas
  • Raghu Bollapragada
  • Jiahao Shi
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Other Topics Tags , ,

    In this paper, we propose a method that has foundations in the line search sequential quadratic programming paradigm for solving general nonlinear equality constrained optimization problems. The method employs a carefully designed modified line search strategy that utilizes second-order information of both the objective and constraint functions, as required, to mitigate the Maratos effect. Contrary … Read more

    A Stochastic Objective-Function-Free Adaptive Regularization Method with Optimal Complexity

  • Serge Gratton
  • Sadok Jerad
  • Philippe L. Toint
    • Categories Data Science Algorithms, Nonlinear Optimization Tags , , , ,

    A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex optimization is presented which never computes the objective-function value, but yet achieves the optimal $\mathcal{O}(\epsilon^{-3/2})$ complexity bound for finding first-order critical points. The method is noise-tolerant and the inexactness conditions required for convergence depend on the history of past steps. Applications to cases where derivative evaluation … Read more

    BattOpt: Optimal Facility Planning for Electric Vehicle Battery Recycling

  • Matthew Brun
  • Xu Andy Sun
    • Categories Energy, Global Optimization Applications, Stochastic Programming Tags , , ,

    The electric vehicle (EV) battery supply chain will face challenges in sourcing scarce and expensive minerals required for manufacturing and in disposing of hazardous retired batteries. Integrating recycling technology into the supply chain has the potential to alleviate these issues; however, players in the battery market must design investment plans for recycling facilities. In this … Read more

    A Unified Approach for Maximizing Continuous $\gamma$-weakly DR-submodular Functions

  • Mohammad Pedramfar
  • Christopher Quinn
  • Vaneet Aggarwal
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , ,

    This paper presents a unified approach for maximizing continuous \(\gamma\)-weakly DR-submodular functions that encompasses a range of settings and oracle access types. Our approach includes a Frank-Wolfe type offline algorithm for both monotone and non-monotone functions, with different restrictions on the convex feasible region. We consider settings where the oracle provides access to either the … Read more

    Doubly stochastic primal dual splitting algorithm with variance reduction for saddle point problems

  • Dimitri Papadimitriou
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Nonlinear Optimization, Unconstrained Optimization Tags , , , , ,

    The structured saddle-point problem involving the infimal convolution in real Hilbert spaces finds applicability in many applied mathematics disciplines. For this purpose, we develop a stochastic primal-dual splitting algorithm with loopless variance-reduction for solving this generic problem. We first prove the weak almost sure convergence of the iterates. We then demonstrate that our algorithm achieves … Read more

    Almost-sure convergence of iterates and multipliers in stochastic sequential quadratic optimization

  • Frank E. Curtis
  • Xin Jiang
  • Qi Wang
    • Categories Constrained Nonlinear Optimization, Data Science Applications, Stochastic Programming Tags , , ,

    Stochastic sequential quadratic optimization (SQP) methods for solving continuous optimization problems with nonlinear equality constraints have attracted attention recently, such as for solving large-scale data-fitting problems subject to nonconvex constraints. However, for a recently proposed subclass of such methods that is built on the popular stochastic-gradient methodology from the unconstrained setting, convergence guarantees have been … Read more

    Asynchronous Iterations in Optimization: New Sequence Results and Sharper Algorithmic Guarantees

  • Hamid Reza Feyzmahdavian
  • Mikael Johansson
    • Categories Convex Optimization, Global Optimization, Parallel Algorithms Tags , , , ,

    We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony impacts the convergence rates of the iterates. Our results shorten, streamline and strengthen existing convergence proofs for several asynchronous optimization … Read more

    A Stochastic-Gradient-based Interior-Point Algorithm for Solving Smooth Bound-Constrained Optimization Problems

  • Qi Wang
  • Frank E. Curtis
  • Daniel P. Robinson
  • Vyacheslav Kungurtsev
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization in Data Science Tags , ,

    A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results. The algorithm is unique from other interior-point methods for solving smooth (nonconvex) optimization problems since the search directions are computed using stochastic gradient estimates. It is also unique … Read more

    Multi-model Partially Observable Markov Decision Processes

  • Weiyu Li
  • Brian T. Denton
    • Categories Applications - OR and Management Sciences, Biomedical Applications, Stochastic Programming Tags , , ,

    We propose a new multi-model partially observable Markov decision process (MPOMDP) model to address the issue of model ambiguity in partially observable Markov decision process. Here, model ambiguity is defined as the case where there are multiple credible optimization models with the same structure but different model parameters. The proposed MPOMDP model aims to learn … Read more