A Sparsity Preserving Convexification Procedure for Indefinite Quadratic Programs Arising in Direct Optimal Control

  • Moritz Diehl
  • Rien Quirynen
  • Robin Verschueren
  • Mario Zanon
    • Categories Systems governed by Differential Equations Optimization Tags , ,

    Quadratic programs (QP) with an indefinite Hessian matrix arise naturally in some direct optimal control methods, e.g. as subproblems in a sequential quadratic programming (SQP) scheme. Typically, the Hessian is approximated with a positive definite matrix to ensure having a unique solution; such a procedure is called \emph{regularization}. We present a novel regularization method tailored … Read more

    Primal-dual potential reduction algorithm for symmetric programming problems with nonlinear objective functions

  • Leonid Faybusovich
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , ,

    We consider a primal-dual potential reduction algorithm for nonlinear convex optimization problems over symmetric cones. The same complexity estimates as in the case of linear objective function are obtained provided a certain nonlinear system of equations can be solved with a given accuracy. This generalizes the result of K. Kortanek, F. Potra and Y.Ye. We … Read more

    Guaranteed Bounds for General Non-discrete Multistage Risk-Averse Stochastic Optimization Programs

  • Francesca Maggioni
  • Georg Ch. Pflug
    • Categories Stochastic Programming Tags , , , , ,

    In general, multistage stochastic optimization problems are formulated on the basis of continuous distributions describing the uncertainty. Such ”infinite” problems are practically impossible to solve as they are formulated and finite tree approximations of the underlying stochastic processes are used as proxies. In this paper, we demonstrate how one can find guaranteed bounds, i.e. finite … Read more

    A dual-ascent-based branch-and-bound framework for the prize-collecting Steiner tree and related problems

  • Markus Leitner
  • Ivana Ljubić
  • Martin Luipersbeck
  • Markus Sinnl
    • Categories Combinatorial Optimization, Integer Programming, Network Optimization Tags , , , ,

    In this work we present a branch-and-bound (B&B) framework for the asymmetric prize-collecting Steiner tree problem (APCSTP). Several well-known network design problems can be transformed to the APCSTP, including the Steiner tree problem (STP), prize-collecting Steiner tree problem (PCSTP), maximum-weight connected subgraph problem (MWCS) and the node-weighted Steiner tree problem (NWSTP). The main component of … Read more

    Exact Worst-case Performance of First-order Methods for Composite Convex Optimization

  • François Glineur
  • Julien M. Hendrickx
  • Adrien B. Taylor
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , , , , , , ,

    We provide a framework for computing the exact worst-case performance of any algorithm belonging to a broad class of oracle-based first-order methods for composite convex optimization, including those performing explicit, projected, proximal, conditional and inexact (sub)gradient steps. We simultaneously obtain tight worst-case guarantees and explicit instances of optimization problems on which the algorithm reaches this … Read more

    Convergence Analysis of ISTA and FISTA for “Strongly + Semi” Convex Programming

  • Ke Guo
  • Xiao-Ming Yuan
  • Shangzhi Zeng
    • Categories Convex Optimization Tags , , , , ,

    The iterative shrinkage/thresholding algorithm (ISTA) and its faster version FISTA have been widely used in the literature. In this paper, we consider general versions of the ISTA and FISTA in the more general “strongly + semi” convex setting, i.e., minimizing the sum of a strongly convex function and a semiconvex function; and conduct convergence analysis … Read more

    Multi-Period Portfolio Optimization: Translation of Autocorrelation Risk to Excess Variance

  • Byung-Geun Choi
  • Ruiwei Jiang
  • Napat Rujeerapaiboon
    • Categories Finance and Economics, Robust Optimization, Stochastic Programming Tags , , ,

    Growth-optimal portfolios are guaranteed to accumulate higher wealth than any other investment strategy in the long run. However, they tend to be risky in the short term. For serially uncorrelated markets, similar portfolios with more robust guarantees have been recently proposed. This paper extends these robust portfolios by accommodating non-zero autocorrelations that may reflect investors’ … Read more

    An Adaptive Discretization MINLP Algorithm for Optimal Synthesis of Decentralized Energy Supply Systems

  • Björn Bahl
  • André Bardow
  • Arie M.C.A. Koster
  • Marco E. Lübbecke
  • Sebastian Goderbauer
  • Philip Voll
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering Tags , , , ,

    Decentralized energy supply systems (DESS) are highly integrated and complex systems designed to meet time-varying energy demands, e.g., heating, cooling, and electricity. The synthesis problem of DESS addresses combining various types of energy conversion units, choosing their sizing and operations to maximize an objective function, e.g., the net present value. In practice, investment costs and … Read more

    DESSLib – Benchmark Instances for Optimization of Decentralized Energy Supply Systems

  • Fritz Arnold
  • Björn Bahl
  • André Bardow
  • Arie M.C.A. Koster
  • Marco E. Lübbecke
  • Sebastian Goderbauer
  • Philip Voll
    • Categories Applications - Science and Engineering Tags , , , , , ,

    DESSLib (http://www.math2.rwth-aachen.de/DESSLib) provides benchmark instances obtained by real world data for synthesis problems of decentralized energy supply systems (DESS). In this paper, the considered optimization problem is described in detail. For a description of the functions and parameters used to describe the system and equipment, see the documentation found on DESSLib website http://www.math2.rwth-aachen.de/DESSLib. Article Download … Read more

    The proximal point method for locally Lipschitz functions in multiobjective optimization

  • Glaydston Bento
  • João Xavier da Cruz Neto
  • Antoine Soubeyran
  • João Carlos Souza
  • G. López
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , , , , ,

    This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by Bonnel et al. (SIAM J. Optim., 4 (2005), pp. 953-970) is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new approach for convergence analysis of the … Read more