Hidden convexity, optimization, and algorithms on rotation matrices

  • Kevin Shu
  • Alex L. Wang
  • Akshay Ramachandran
    • Categories Constrained Nonlinear Optimization, Other Topics, Semi-definite Programming Tags , ,

    This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices \(\text{SO}(n)\). Such problems are nonconvex due to the constraint\(X\in\text{SO}(n)\). Nonetheless, we show that certain linear images of \(\text{SO}(n)\) are convex, opening up the possibility for convex optimization algorithms with provable guarantees for these problems. Our main technical contributions … Read more

    Jordan automorphisms and derivatives of symmetric cones

  • Michael Orlitzky
    • Categories Cone Programming Tags , , , ,

    Hyperbolicity cones, and in particular symmetric cones, are of great interest in optimization. Renegar showed that every hyperbolicity cone has a family of derivative cones that approximate it. Ito and Lourenço found the automorphisms of those derivatives when the original cone is generated by rank-one elements, as symmetric cones happen to be. We show that … Read more

    Data-driven distributionally robust optimization: Intersecting ambiguity sets, performance analysis and tractability

  • Neda Tanoumand
  • Merve Bodur
  • Joe Naoum-Sawaya
    • Categories Robust Optimization Tags , , ,

    We consider stochastic programs in which the probability distribution of uncertain parameters is unknown and partial information about it can only be captured from limited data. We use distributionally robust optimization (DRO) to model such problems. As opposed to the commonly used approach for DRO problems that suggests creating an ambiguity set by following a specific … Read more

    Application of a Gas Market Model with Linear Programming. The Influence of the Dollar Exchange Rate on the Wholesale Price of Natural Gas in Northwest Europe until 2040

  • Maik Günther
    • Categories Finance and Economics, Linear Programming, Optimization of Simulated Systems Tags , , , , , , , , ,

    The price of natural gas at wholesale markets in Northwest Europe is influenced by numerous parameters. The USD to EUR exchange rate is one of these parameters. Using the LP-based gas market model WEGA, this paper will examine the impact of USD exchange rates on wholesale natural gas prices in Northwest Europe from 2025 to … Read more

    An active set method for bound-constrained optimization

  • Arnold Neumaier
  • Behzad Azmi
  • Morteza Kimiaei
    • Categories Bound-constrained Optimization, Nonlinear Optimization Tags

    In this paper, a class of algorithms is developed for bound-constrained optimization. The new scheme uses the gradient-free line search along bent search paths. Unlike traditional algorithms for bound-constrained optimization, our algorithm ensures that the reduced gradient becomes arbitrarily small. It is also proved that all strongly active variables are found and fixed after finitely … Read more

    Algorithms for Cameras View-Frame Placement Problems in the Presence of an Adversary and Distributional Ambiguity

  • Seonghun Park
  • Manish Bansal
    • Categories Combinatorial Optimization, Game Theory, Stochastic Programming Tags , , ,

    In this paper, we introduce cameras view-frame placement problem (denoted by CFP) in the presence an adversary whose objective is to minimize the maximum coverage by p cameras in response to input provided by n autonomous agents in a remote location. We allow uncertainty in the success of attacks, incomplete information of the probability distribution … Read more

    Optimal Planning for the Electrification of Bus Fleets in Public Transit Systems

  • Filipe Cabral
  • Xu Andy Sun
    • Categories Applications - OR and Management Sciences, Integer Programming, Transportation Tags , , ,

    Electric vehicles (EV) pave a promising way towards low-carbon transportation, but the transition to all EV fleets creates new challenges for the public transportation sector. Despite increasing adoption of electric buses, the main challenges presented by the battery electric bus technology include the lack of charging facilities, the reduced operating capacity per battery charge compared … Read more

    Closing Duality Gaps of SDPs through Perturbation

  • Takashi Tsuchiya
  • Bruno F. Lourenço
  • Masakazu Muramatsu
  • Takayuki Okuno
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , , , ,

    Let \(({\bf P},{\bf D})\) be a primal-dual pair of SDPs with a nonzero finite duality gap. Under such circumstances, \({\bf P}\) and \({\bf D}\) are weakly feasible and if we perturb the problem data to recover strong feasibility, the (common) optimal value function \(v\) as a function of the perturbation is not well-defined at zero … Read more

    Markov Decision Process Design: A Framework for Integrating Strategic and Operational Decisions

  • Seth Brown
  • Saumya Sinha
  • Andrew J. Schaefer
    • Categories Integer Programming, Nonlinear Optimization Tags , ,

    We consider the problem of optimally designing a system for repeated use under uncertainty. We develop a modeling framework that integrates design and operational phases, which are represented by a mixed-integer program and discounted-cost infinite-horizon Markov decision processes, respectively. We seek to simultaneously minimize the design costs and the subsequent expected operational costs. This problem … Read more

    Characterizing Rational Transplant Program Response to Outcome-Based Regulation

  • David T. Mildebrath
  • Taewoo Lee
  • Saumya Sinha
  • Andrew J. Schaefer
    • Categories Applications - OR and Management Sciences Tags , , ,

    Organ transplantation is an increasingly common therapy for many types of end-stage organ failure, including lungs, hearts, kidneys and livers. The past twenty years have seen increased scrutiny of post-transplant outcomes in the United States, in order to ensure the efficient utilization of the scarce organ supply. Under regulations by the Organ Procurement Transplantation Network … Read more