Advancements in the computation of enclosures for multi-objective optimization problems

A central goal for multi-objective optimization problems is to compute their nondominated sets. In most cases these sets consist of infinitely many points and it is not a practical approach to compute them exactly. One solution to overcome this problem is to compute an enclosure, a special kind of coverage, of the nondominated set. One … Read more

Distributionally Robust Disaster Relief Planning under the Wasserstein Set

We study a two-stage natural disaster management problem modeled as a stochastic program, where the first stage consists of a facility location problem, deciding where to open facilities and pre-allocate resources such as medical and food kits, and the second stage is a fixed-charge transportation problem, routing resources to affected areas after observing a disaster. … Read more

Accelerating Stochastic Sequential Quadratic Programming for Equality Constrained Optimization using Predictive Variance Reduction

In this paper, we propose a stochastic variance reduction method for solving equality constrained optimization problems. Specifically, we develop a method based on the sequential quadratic programming paradigm that utilizes gradient approximations via predictive variance reduction techniques. Under reasonable assumptions, we prove that a measure of first-order stationarity evaluated at the iterates generated by our … Read more

Dynamic programming in convex stochastic optimization

This paper studies the dynamic programming principle for general convex stochastic optimization problems introduced by Rockafellar and Wets in the 1970s. We extend the applicability of the theory by relaxing compactness and boundedness assumptions. In the context of financial mathematics, the relaxed assumptions are satisfied under the well-known no-arbitrage condition and the reasonable asymptotic elasticity … Read more

Courier satisfaction in rapid delivery systems using dynamic operating regions

Rapid delivery systems where an order is delivered to a customer from a local distribution point within minutes or hours have experienced rapid growth recently and often rely on gig economy couriers. The prime example is a meal delivery system. During an operating day, couriers in such a system are used to deliver orders placed … Read more

An Adaptive Riemannian Gradient Method Without Function Evaluations

In this paper we propose an adaptive gradient method for optimization on Riemannian manifolds. The update rule for the stepsizes relies only on gradient evaluations. Assuming that the objective function is bounded from below and that its gradient field is Lipschitz continuous, we establish worst-case complexity bounds for the number of gradient evaluations that the … Read more

Benders-type Branch-and-Cut Algorithms for Capacitated Facility Location with Single-Sourcing

We consider the capacitated facility location problem with (partial) single-sourcing (CFLP-SS). A natural mixed integer formulation for the problem involves 0-1 variables x_j indicating whether faclility j is used or not and y_{ij} variables indicating the fraction of the demand of client i that is satisfied from facility j. When the x variables are fixed, … Read more

Direct search based on probabilistic descent in reduced spaces

Derivative-free algorithms seek the minimum value of a given objective function without using any derivative information. The performance of these methods often worsen as the dimension increases, a phenomenon predicted by their worst-case complexity guarantees. Nevertheless, recent algorithmic proposals have shown that incorporating randomization into otherwise deterministic frameworks could alleviate this effect for direct-search methods. … Read more

A Decomposition Algorithm for Two-Stage Stochastic Programs with Nonconvex Recourse

In this paper, we have studied a decomposition method for solving a class of nonconvex two-stage stochastic programs, where both the objective and constraints of the second-stage problem are nonlinearly parameterized by the first-stage variable. Due to the failure of the Clarke regularity of the resulting nonconvex recourse function, classical decomposition approaches such as Benders … Read more

Optimizing investment allocation: a combination of Logistic Regression and Markowitz model

One of the biggest challenges in quantitative finance is the efficient allocation of capital. Thus, in this study, a two-step methodology was proposed, in which a combination of logistic regression and Markowitz model was performed to determine optimized portfolios. In this context, in the first step, fundamentalist indicators were used as inputs to the logistic … Read more