Relations Between Abs-Normal NLPs and MPCCs Part 2: Weak Constraint Qualifications

  • Lisa Hegerhorst-Schultchen
  • Christian Kirches
  • Marc C. Steinbach
    • Categories Nonsmooth Optimization Tags , , , ,

    This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie’s and Guignard’s kink qualification and … Read more

    Gaining traction – On the convergence of an inner approximation scheme for probability maximization

  • Csaba I. Fábián
    • Categories Convex Optimization, Stochastic Programming Tags ,

    We analyze an inner approximation scheme for probability maximization. The approach was proposed in Fabian, Csizmas, Drenyovszki, Van Ackooij, Vajnai, Kovacs, Szantai (2018) Probability maximization by inner approximation, Acta Polytechnica Hungarica 15:105-125, as an analogue of a classic dual approach in the handling of probabilistic constraints. Even a basic implementation of the maximization scheme proved … Read more

    Computational Enhancement in the Application of the Branch and Bound Method for Linear Integer Programs and Related Models

  • Ali Al-Hasani
  • Andrew C. Eberhard
  • Masar Al-Rabeeah
  • Santosh Kumar
  • Elias Munapo
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , , , , ,

    In this paper, a reformulation that was proposed for a knapsack problem has been extended to single and bi-objective linear integer programs. A further reformulation by adding an upper bound constraint for a knapsack problem is also proposed and extended to the bi-objective case. These reformulations significantly reduce the number of branch and bound iterations … Read more

    Error Bounds and Singularity Degree in Semidefinite Programming

  • Stefan Sremac
  • Henry Wolkowicz
  • Hugo J. Woerdeman
    • Categories Convex Optimization, Semi-definite Programming Tags , , ,

    In semidefinite programming a proposed optimal solution may be quite poor in spite of having sufficiently small residual in the optimality conditions. This issue may be framed in terms of the discrepancy between forward error (the unmeasurable `true error’) and backward error (the measurable violation of optimality conditions). In his seminal work, Sturm provided an … Read more

    Distributionally Robust Optimization: A Review

  • Hamed Rahimian
  • Sanjay Mehrotra
    • Categories Robust Optimization, Stochastic Programming

    The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. … Read more

    Methods for multiobjective bilevel optimization

  • Gabriele Eichfelder
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization

    This paper is on multiobjective bilevel optimization, i.e. on bilevel optimization problems with multiple objectives on the lower or on the upper level, or even on both levels. We give an overview on the major optimality notions used in multiobjective optimization. We provide characterization results for the set of optimal solutions of multiobjective optimization problems … Read more

    A massively parallel interior-point solver for linear energy system models with block structure

  • Ambros Gleixner
  • Thorsten Koch
  • Hannes Hobbie
  • Domink Möst
  • Daniel Rehfeldt
  • David Schönheit
    • Categories Linear Programming

    Linear energy system models are often a crucial component of system design and operations, as well as energy policy consulting. Such models can lead to large-scale linear programs, which can be intractable even for state-of-the-art commercial solvers—already the available memory on a desktop machine might not be sufficient. Against this backdrop, this article introduces an … Read more

    Competing Objective Optimization in Networked Swarm Systems

  • Md Ali Azam
  • Shawon Dey
  • Hans D Mittelmann
  • Shankarachary Ragi
    • Categories Applications - Science and Engineering Tags , , ,

    In this paper, we develop a decentralized collaborative sensing algorithm where the sensors are located on-board autonomous unmanned aerial vehicles. We develop this algorithm in the context of a target tracking application, where the objective is to maximize the tracking performance measured by the meansquared error between the target state estimate and the ground truth. … Read more

    A Data Efficient and Feasible Level Set Method for Stochastic Convex Optimization with Expectation Constraints

  • Qihang Lin
  • Selvaprabu Nadarajah
  • Negar Soheili
  • Tianbao Yang
    • Categories Convex Optimization, Stochastic Programming Tags , , ,

    Stochastic convex optimization problems with expectation constraints (SOECs) are encountered in statistics and machine learning, business, and engineering. In data-rich environments, the SOEC objective and constraints contain expectations defined with respect to large datasets. Therefore, efficient algorithms for solving such SOECs need to limit the fraction of data points that they use, which we refer … Read more

    Benders Decomposition with Adaptive Oracles for Large Scale Optimization

  • Andreas Grothey
  • Kenneth McKinnon
  • Nicolò Mazzi
  • Nagisa Sugishita
    • Categories Applications - OR and Management Sciences Tags , , ,

    This paper proposes an algorithm to efficiently solve large optimization problems which exhibit a column bounded block-diagonal structure, where subproblems differ in right-hand side and cost coefficients. Similar problems are often tackled using cutting-plane algorithms, which allow for an iterative and decomposed solution of the problem. When solving subproblems is computationally expensive and the set … Read more