On the use of Jordan Algebras for improving global convergence of an Augmented Lagrangian method in nonlinear semidefinite programming

  • Roberto Andreani
  • Ellen H. Fukuda
  • Gabriel Haeser
  • Daiana O. Santos
  • Leonardo D. Secchin
    • Categories Nonlinear Optimization, Semi-definite Programming Tags , , , ,

    Jordan Algebras are an important tool for dealing with semidefinite programming and optimization over symmetric cones in general. In this paper, a judicious use of Jordan Algebras in the context of sequential optimality conditions is done in order to generalize the global convergence theory of an Augmented Lagrangian method for nonlinear semidefinite programming. An approximate … Read more

    Optimizing Diesel Fuel Supply Chain Operations for Hurricane Relief

  • Daniel Duque
  • David P. Morton
  • Haoxiang Yang
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , ,

    Hurricanes can cause severe property damage and casualties in coastal regions. Diesel fuel plays a crucial role in hurricane disaster relief. It is important to optimize fuel supply chain operations so that emergency demand for diesel can be mitigated in a timely manner. However, it can be challenging to estimate demand for fuel and make … Read more

    Decomposition Algorithms for Some Deterministic and Two-Stage Stochastic Single-Leader Multi-Follower Games

  • Pedro Borges de Melo
  • Claudia Sagastizábal
  • Mikhail V. Solodov
    • Categories Complementarity and Variational Inequalities, Nonsmooth Optimization, Stochastic Programming Tags , , , , ,

    We consider a certain class of hierarchical decision problems that can be viewed as single-leader multi-follower games, and be represented by a virtual market coordinator trying to set a price system for traded goods, according to some criterion that balances supply and demand. The objective function of the market coordinator involves the decisions of many … Read more

    A Primal–Dual Penalty Method via Rounded Weighted-\boldmath{$\ell_1$} Lagrangian Duality

  • Regina S. Burachik
  • Christopher J. Price
  • C. Yalcin Kaya
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization

    We propose a new duality scheme based on a sequence of smooth minorants of the weighted-$\ell_1$ penalty function, interpreted as a parametrized sequence of augmented Lagrangians, to solve nonconvex and nonsmooth constrained optimization problems. For the induced sequence of dual problems, we establish strong asymptotic duality properties. Namely, we show that (i) the sequence of … Read more

    On Inexact Accelerated Proximal Gradient Methods with Relative Error Rules

  • Yunier Bello-Cruz
  • Max L. N. Gonçalves
  • Nathan Krislock
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , ,

    One of the most popular and important first-order iterations that provides optimal complexity of the classical proximal gradient method (PGM) is the “Fast Iterative Shrinkage/Thresholding Algorithm” (FISTA). In this paper, two inexact versions of FISTA for minimizing the sum of two convex functions are studied. The proposed schemes inexactly solve their subproblems by using relative … Read more

    Aid Allocation for Camp-Based and Urban Refugees with Uncertain Demand and Replenishments

  • Shima Azizi
  • Cem Deniz Caglar Bozkir
  • Andrew C. Trapp
  • O. Erhun Kundakcioglu
  • Ali Kaan Kurbanzade
    • Categories Applications - OR and Management Sciences Tags , , ,

    There are nearly 26 million refugees worldwide seeking safety from persecution, violence, conflict, and human rights violations. Camp-based refugees are those that seek shelter in refugee camps, whereas urban refugees inhabit nearby, surrounding populations. The systems that supply aid to refugee camps may suffer from ineffective distribution due to challenges in administration, demand uncertainty and … Read more

    Parametric analysis of conic linear optimization

  • Guo Jinhai
  • Yan Zizong
  • Li Xiangjun
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , , , ,

    This paper focuses on the parametric analysis of a conic linear optimization problem with respect to the perturbation of the objective function along many fixed directions. We introduce the concept of the primal and dual conic linear inequality representable sets, which is very helpful for converting the correlation of the parametric conic linear optimization problems … Read more

    Optimising the assignment of swabs and reagents for PCR testing during a viral epidemic

  • Alberto Santini
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering Tags , ,

    Early large-scale swab testing is a fundamental tool for health authorities to assess the prevalence of a virus and enact appropriate mitigation measures during an epidemic. The COVID-19 pandemic has shown that the availability of chemical reagents required to carry out the tests is often a bottleneck in increasing a country’s testing capacity. Further, demand … Read more

    Towards practical generic conic optimization

  • Chris Coey
  • Juan Pablo Vielma
  • Lea Kapelevich
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems Tags , , ,

    Many convex optimization problems can be represented through conic extended formulations with auxiliary variables and constraints using only the small number of standard cones recognized by advanced conic solvers such as MOSEK 9. Such extended formulations are often significantly larger and more complex than equivalent conic natural formulations, which can use a much broader class … Read more

    Interdependence and Integration among Components of the Airline Scheduling Process: A State-of-the-Art Review

  • Divyam Aggarwal
  • Michael T. M. Emmerich
  • Dhish K. Saxena
    • Categories Airline Optimization, Scheduling, Transportation Tags , , , , , ,

    Over the last few decades, the Airline Scheduling Process (ASP) has received an unprecedented attention from airliners and operations research society. Conventionally, the Airline Scheduling Process is decomposed into four sub-problems namely-Schedule Generation, Fleet Assignment, aircraft Routing, and Crew Scheduling which are solved sequentially in order to incorporate tractability and feasibility in the overall process. … Read more