This is the home page of the Open Journal of Mathematical Optimization, an electronic journal of computer science and mathematics owned by its Editorial Board.

The Open Journal of Mathematical Optimization (OJMO) publishes original and high-quality articles dealing with every aspect of mathematical optimization, ranging from numerical and computational aspects to the theoretical questions related to mathematical optimization problems. The topics covered by the journal are classified into four areas:

  1. Continuous Optimization
  2. Discrete Optimization
  3. Optimization under Uncertainty
  4. Computational aspects and applications

The journal publishes high-quality articles in open access free of charge, meaning that neither the authors nor the readers have to pay to access the content of the published papers, thus adhering to the principles of Fair Open Access. The journal supports open data and open code whenever possible and authors are strongly encouraged to submit code and data sets along with their manuscript.


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e-ISSN : 2777-5860

New articles

Estimating Shape Parameters of Piecewise Linear-Quadratic Problems

Piecewise Linear-Quadratic (PLQ) penalties are widely used to develop models in statistical inference, signal processing, and machine learning. Common examples of PLQ penalties include least squares, Huber, Vapnik, 1-norm, and their asymmetric generalizations. Properties of these estimators depend on the choice of penalty and its shape parameters, such as degree of asymmetry for the quantile loss, and transition point between linear and quadratic pieces for the Huber function.

In this paper, we develop a statistical framework that can help the modeler to automatically tune shape parameters once the shape of the penalty has been chosen. The choice of the parameter is informed by the basic notion that each PLQ penalty should correspond to a true statistical density. The normalization constant inherent in this requirement helps to inform the optimization over shape parameters, giving a joint optimization problem over these as well as primary parameters of interest. A second contribution is to consider optimization methods for these joint problems. We show that basic first-order methods can be immediately brought to bear, and design specialized extensions of interior point (IP) methods for PLQ problems that can quickly and efficiently solve the joint problem. Synthetic problems and larger-scale practical examples illustrate the utility of the approach. Code for the new IP method is implemented using the Julia language (

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Gradient formulae for probability functions depending on a heterogenous family of constraints

Probability functions measure the degree of satisfaction of certain constraints that are impacted by decisions and uncertainty. Such functions appear in probability or chance constraints ensuring that the degree of satisfaction is sufficiently high. These constraints have become a very popular modelling tool and are indeed intuitively easy to understand. Optimization problems involving probabilistic constraints have thus arisen in many sectors of the industry, such as in the energy sector. Finding an efficient solution methodology is important and first order information of probability functions play a key role therein. In this work we are motivated by probability functions measuring the degree of satisfaction of a potentially heterogenous family of constraints. We suggest a framework wherein each individual such constraint can be analyzed structurally. Our framework then allows us to establish formulae for the generalized subdifferential of the probability function itself. In particular we formally establish a (sub)-gradient formulæ for probability functions depending on a family of non-convex quadratic inequalities. The latter situation is relevant for gas-network applications.

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