The purpose of this paper is to completely characterize the global approximate optimality (ε-optimality) in reverse convex optimization under the general nonconvex constraint “h(x) ≥ 0″. The main condition presented is obtained in terms of Fenchel’s ε-subdifferentials thanks to El Maghri’s ε-efficiency in difference vector optimization [J. Glob. Optim. 61 (2015) 803–812], after converting the … Read more
Stochastic optimization is often hampered by distributional ambiguity, where critical probability distributions are poorly characterized or unknown. Addressing this challenge, we introduce a new framework that targets the minimization of a statistical upper bound for the expected value of uncertain objectives, facilitating more statistically robust decision-making. Central to our approach is the Average Percentile Upper … Read more
In this work we show how exploiting black-box optimization in the design of a cooling system for a nozzle in a gas turbine. We develop a black-box function that simulates an impingement cooling system starting from a well-known model that correlates the design features of the cooling system with efficiency parameters. We also provide a … Read more
Abstract: In a real Hilbert space domain setting, we study the convergence properties of the stochastic Ravine accelerated gradient method for convex differentiable optimization. We consider the general form of this algorithm where the extrapolation coefficients can vary with each iteration, and where the evaluation of the gradient is subject to random errors. This general … Read more
A common strategy for solving an unconstrained two-player Nash equilibrium problem with continuous variables is applying Newton’s method to the system obtained by the corresponding first-order necessary optimality conditions. However, when taking into account the game dynamics, it is not clear what is the goal of each player when considering they are taking their current … Read more
The effectiveness of machine learning (ML) algorithms is deeply intertwined with the quality and diversity of their training datasets. Improved datasets, marked by superior quality, enhance the predictive accuracy and broaden the applicability of models across varied scenarios. Researchers often integrate data from multiple sources to mitigate biases and limitations of single-source datasets. However, this … Read more
We introduce a polyhedral framework for characterizing instances of quadratic combinatorial optimization programs (QCOPs) that are linearizable, meaning that the quadratic objective can be equivalently rewritten as linear in such a manner that preserves the objective function value at all feasible solutions. In particular, we show that an instance is linearizable if and only if … Read more
A multiobjective stochastic convex quadratic program (MOSCQP) is a multiobjective optimization problem with convex quadratic objectives that are observed with stochastic error. MOSCQP is a useful problem formulation arising, for example, in model calibration and nonlinear system identification when a single regression model combines data from multiple distinct sources, resulting in a multiobjective least squares … Read more