Numerical optimization in complex numbers has drawn much less attention than in real numbers. A widespread opinion is that, since a complex number is a pair of real numbers, the best strategy to solve a complex optimization problem is to transform it into real numbers and to solve the latter by a real number solver. … Read more
We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [1] by taking a different perspective, leading to an algorithm which is conceptually more natural, has notably improved convergence rates, and for which the analysis … Read more
Maritime transportation plays a crucial role in the international economy. Port container terminals around the world compete to attract more traffic and are forced to offer better quality of service. This entails reducing operating costs and vessel service times. In doing so, one of the most important problems they face is the Berth Allocation and … Read more
This paper addresses the Entropic Value-at-Risk (EVaR), a recently introduced coherent risk measure. It is demonstrated that the norms induced by EVaR induce the same Banach spaces, irrespective of the confidence level. Three spaces, called the primal, dual, and bidual entropic spaces, corresponding with EVaR are fully studied. It is shown that these spaces equipped … Read more
Motivated by its implications in the development of general purpose solvers for decomposable Mixed Integer Programs (MIP), we address a fundamental research question, that is to assess if good decomposition patterns can be consistently found by looking only at static properties of MIP input instances, or not. We adopt a data driven approach, devising a … Read more
The purpose of this paper is to provide strong reformulations for binary quadratic problems. We propose a first methodological analysis on a family of reformulations combining Dantzig-Wolfe decomposition and Quadratic Convex Reformulation principles. As a representative case study, we apply them to a cardinality constrained quadratic knapsack problem, providing extensive experimental insights. We show that … Read more
The proximal point algorithm (PPA) is a fundamental method for convex programming. When PPA applied to solve linearly constrained convex problems, we may prefer to choose an appropriate metric matrix to define the proximal regularization, so that the computational burden of the resulted PPA can be reduced, and in most cases, even admit closed form … Read more
We point out an omission in the paper ‘The Algebraic Structure of the Arbitrary-Order Cone’ by Alzalg published in J. Optim. Theory Appl. in 2016. In reaction to this omission, some alternative results have been presented. Article Download View A Comment on the Paper `The Algebraic Structure of the Arbitrary-Order Cone'
We propose a randomized gradient method – or a randomized cutting-plane method from a dual viewpoint. From the primal viewpoint, our method bears a resemblance to the stochastic approximation family. But in contrast to stochastic approximation, the present method builds a model problem. Citation Kecskemet College, Pallasz Athene University. Izsaki ut 10, 6000 Kecskemet, Hungary; … Read more
Scenarios are indispensable ingredients for the numerical solution of stochastic optimization problems. Earlier approaches for optimal scenario generation and reduction are based on stability arguments involving distances of probability measures. In this paper we review those ideas and suggest to make use of stability estimates based on distances containing minimal information, i.e., on data appearing … Read more