Co-optimization of Demand Response and Reserve Offers for a Major Consumer

In this paper we present a stochastic optimization problem for a strategic major consumer who has flexibility over its consumption and can offer reserve. Our model is a bi-level optimization model (reformulated as a mixed-integer program) that embeds the optimal power flow problem, in which electricity and reserve are co-optimized. We implement this model for … Read more

A Novel Approach for Solving Convex Problems with Cardinality Constraints

In this paper we consider the problem of minimizing a convex differentiable function subject to sparsity constraints. Such constraints are non-convex and the resulting optimization problem is known to be hard to solve. We propose a novel generalization of this problem and demonstrate that it is equivalent to the original sparsity-constrained problem if a certain … Read more

A hybrid approach for Bi-Objective Optimization

A large number of the real world planning problems which are today solved using Operations Research methods are actually multi-objective planning problems, but most of them are solved using single-objective methods. The reason for converting, i.e. simplifying, multi- objective problems to single-objective problems is that no standard multi-objective solvers exist and specialized algorithms need to … Read more

Plea for a semidefinite optimization solver in complex numbers

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

Radial Subgradient Descent

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

A Biased Random-Key Genetic Algorithm for the Berth Allocation and Quay Crane Assignment Problem

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

An Analytical Study of Norms and Banach Spaces Induced by the Entropic Value-at-Risk

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

Random Sampling and Machine Learning to Understand Good Decompositions

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

Dantzig Wolfe decomposition and objective function convexification for binary quadratic problems: the cardinality constrained quadratic knapsack case

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

On Relaxation of Some Customized Proximal Point Algorithms for Convex Minimization: From Variational Inequality Perspective

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