Month: September 2019

Robust Optimization with Decision-Dependent Information Discovery

  • Phebe Vayanos
  • Angelos Georghiou
  • Han Yu
    • Categories Robust Optimization Tags , , ,

    Robust optimization (RO) is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, such as R&D project selection, production planning, or preference elicitation for product or policy recommendations, the time of information discovery is decision-dependent and the uncertain parameters only become observable after an often costly … Read more

    Generalized Gradients in Problems of Dynamic Optimization, Optimal Control, and Machine Learning

  • Vladimir I. Norkin
    • Categories Nonsmooth Optimization, Stochastic Programming Tags , , , , , , ,

    In this work, nonconvex nonsmooth problems of dynamic optimization, optimal control in discrete time (including feedback control), and machine learning are considered from a common point of view. An analogy is observed between tasks of controlling discrete dynamic systems and training multilayer neural networks with nonsmooth target function and connections. Methods for calculating generalized gradients … Read more

    Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach

  • Nadav Hallak
  • Marc Teboulle
    • Categories Constrained Nonlinear Optimization Tags , ,

    This paper introduces a method for computing points satisfying the second-order necessary optimality conditions in constrained nonconvex minimization. The method comprises two independent steps corresponding to the first and second order conditions. The first-order step is a generic closed map algorithm which can be chosen from a variety of first-order algorithms, making it The second-order … Read more

    Distance geometry and data science

  • Leo Liberti
    • Categories Data-Mining, Global Optimization Applications, Graphs and Matroids Tags , , , , ,

    Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in vectorial form. In this survey we discuss the fundamental problem of mapping graphs to vectors, and its … Read more

    On the Convergence to Stationary Points of Deterministic and Randomized Feasible Descent Directions Methods

  • Amir Beck
  • Nadav Hallak
    • Categories Constrained Nonlinear Optimization Tags , ,

    This paper studies the class of nonsmooth nonconvex problems in which the difference between a continuously differentiable function and a convex nonsmooth function is minimized over linear constraints. Our goal is to attain a point satisfying the stationarity necessary optimality condition, defined as the lack of feasible descent directions. Although elementary in smooth optimization, this … Read more

    A Computationally Efficient Algorithm for Computing Convex Hull Prices

  • Anya Castillo
  • Bernard Knueven
  • James Ostrowski
  • Jean-Paul Watson
    • Categories Applications - OR and Management Sciences Tags , , , ,

    Electricity markets worldwide allow participants to bid non-convex production offers. While non-convex offers can more accurately reflect a resource’s capabilities, they create challenges for market clearing processes. For example, system operators may be required to execute side payments to participants whose costs are not covered through energy sales as determined via traditional locational marginal pricing … Read more

    Robust Optimal Aiming Strategies in Concentrated Solar Tower Power Plants

  • Christina Büsing
  • Pascal Richter
  • Jeff Cumpston
  • Fynn Kepp
  • Sascha Kuhnke
    • Categories Robust Optimization Tags , , , ,

    A concentrated solar tower power plant consists of a receiver mounted atop of a central tower and a field of movable mirrors called heliostats. The heliostats concentrate solar radiation onto the receiver where a fluid is heated to produce electricity in a conventional thermodynamic cycle. Aiming strategies are used to assign each heliostat to an … Read more

    A relaxed interior point method for low-rank semidefinite programming problems with applications to matrix completion

  • Stefania Bellavia
  • Jacek Gondzio
  • Margherita Porcelli
    • Categories Nonlinear Systems and Least-Squares, Semi-definite Programming Tags , , ,

    A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal solution, a special nearly low-rank form of all primal iterates is imposed. To accommodate such a (restrictive) … Read more

    Periodical Multistage Stochastic Programs

  • Lingquan Ding
  • Alexander Shapiro
    • Categories Stochastic Programming Tags , , , , ,

    In some applications the considered multistage stochastic programs have a periodical behavior. We show that in such cases it is possible to drastically reduce the number of stages by introducing a periodical analog of the so-called Bellman equations for discounted infinite horizon problems, used in Markov Decision Processes and Stochastic Optimal Control. Furthermore, we describe … Read more

    Mixed-Integer Optimal Control under Minimum Dwell Time Constraints

  • Nicolò Robuschi
  • Sebastian Sager
  • Clemens Zeile
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , , , , ,

    Tailored mixed-integer optimal control policies for real-world applications usually have to avoid very short successive changes of the active integer control. Minimum dwell time constraints express this requirement and can be included into the combinatorial integral approximation decomposition, which solves mixed-integer optimal control problems by solving one continuous nonlinear program and one mixed-integer linear program. … Read more