First- and Second-Order High Probability Complexity Bounds for Trust-Region Methods with Noisy Oracles

In this paper, we present convergence guarantees for a modified trust-region method designed for minimizing objective functions whose value is computed with noise and for which gradient and Hessian estimates are inexact and possibly random. In order to account for the noise, the method utilizes a relaxed step acceptance criterion and a cautious trust-region radius … Read more

Integral Global Optimality Conditions and an Algorithm for Multiobjective Problems

In this work, we propose integral global optimality conditions for multiobjective problems not necessarily differentiable. The integral characterization, already known for single objective problems, are extended to multiobjective problems by weighted sum and Chebyshev weighted scalarizations. Using this last scalarization, we propose an algorithm for obtaining an approximation of the weak Pareto front whose effectiveness … Read more

Distributionally Robust Inventory Management with Advance Purchase Contracts

We propose a distributionally robust inventory model for finding an optimal ordering policy that attains the minimum worst-case expected total cost. In a classical stochastic setting, this problem is typically addressed by dynamic programming and is solved by the famous base-stock policy. This approach however crucially relies on two controversial assumptions: the demands are serially … Read more

Identifiability, the KL property in metric spaces, and subgradient curves

Identifiability, and the closely related idea of partial smoothness, unify classical active set methods and more general notions of solution structure. Diverse optimization algorithms generate iterates in discrete time that are eventually confined to identifiable sets. We present two fresh perspectives on identifiability. The first distills the notion to a simple metric property, applicable not … Read more

Capacity planning with uncertain endogenous technology learning

Optimal capacity expansion requires complex decision-making, often influenced by technology learning, which represents the reduction in expansion cost due to factors such as cumulative installed capacity. However, having perfect foresight over the technology cost reduction is highly unlikely. In this work, we develop a multistage stochastic programming framework to model capacity planning problems with endogenous … Read more

BilevelJuMP.jl: Modeling and Solving Bilevel Optimization in Julia

In this paper we present BilevelJuMP, a new Julia package to support bilevel optimization within the JuMP framework. The package is a Julia library that enables the user to describe both upper and lower-level optimization problems using the JuMP algebraic syntax. Due to the generality and flexibility our library inherits from JuMP’s syntax, our package … Read more

Duality in convex stochastic optimization

This paper studies duality and optimality conditions in general convex stochastic optimization problems introduced by Rockafellar and Wets in \cite{rw76}. We derive an explicit dual problem in terms of two dual variables, one of which is the shadow price of information while the other one gives the marginal cost of a perturbation much like in … Read more

Small polygons with large area

A polygon is {\em small} if it has unit diameter. The maximal area of a small polygon with a fixed number of sides $n$ is not known when $n$ is even and $n\geq14$. We determine an improved lower bound for the maximal area of a small $n$-gon for this case. The improvement affects the $1/n^3$ … Read more

Efficient Use of Quantum Linear System Algorithms in Interior Point Methods for Linear Optimization

Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing methods, especially Quantum Interior Point Methods (QIPMs), to solve convex optimization problems, such as Linear Optimization, Semidefinite Optimization, and Second-order Cone Optimization problems. Most of them have … Read more