A Novel Stepsize for Gradient Descent Method

In this paper, we propose a novel stepsize for the classical gradient descent scheme to solve unconstrained nonlinear optimization problems. We are concerned with the convex and smooth objective without the globally Lipschitz gradient condition. Our new method just needs the locally Lipschitz gradient but still gets the rate $O(\frac{1}{k})$ of $f(x^k)-f_*$ at most. As … Read more

Prescriptive price optimization using optimal regression trees

This paper focuses on prescriptive price optimization, which derives the optimal pricing strategy that maximizes future revenue or profit by using demand forecasting models for multiple products. Prescriptive price optimization requires accurate demand forecasting models because the accuracy of these models has a direct impact on pricing strategies aimed at increasing revenue or profit. However, … Read more

Efficient Discovery of Cost-effective Policies in Sequential, Medical Decision-Making Problems

Cost-effectiveness analysis is widely used by policymakers to prioritize interventions that improve a population’s health. Net monetary benefit (NMB) is a metric used for the comparison of medical care strategies, which converts an intervention’s health-benefits to monetary value using the willingness to pay (WTP) as the exchange rate. There is no universally accepted value for … Read more

Gas Transport Network Optimization: PDE-Constrained Models

The optimal control of gas transport networks was and still is a very important topic for modern economies and societies. Accordingly, a lot of research has been carried out on this topic during the last years and decades. Besides mixed-integer aspects in gas transport network optimization, one of the main challenges is that a physically … Read more

Generating balanced workload allocations in hospitals

As pressure on healthcare systems continues to increase, it is becoming more and more important for hospitals to properly manage the high workload levels of their staff. Ensuring a balanced workload allocation between various groups of employees in a hospital has been shown to contribute considerably towards creating sustainable working conditions. However, allocating work to … Read more

Gas Transport Network Optimization: Mixed-Integer Nonlinear Models

Although modern societies strive towards energy systems that are entirely based on renewable energy carriers, natural gas is still one of the most important energy sources. This became even more obvious in Europe with Russia’s 2022 war against the Ukraine and the resulting stop of gas supplies from Russia. Besides that it is very important … Read more

A Fully Adaptive DRO Multistage Framework Based on MDR for Generation Scheduling under Uncertainty

The growing proliferation of wind power into the power grid achieves a low-cost sustainable electricity supply while introducing technical challenges with associated intermittency. This paper proposes a fully adaptive distributionally robust multistage framework based on mixed decision rules (MDR) for generation scheduling under uncertainty to adapt wind power respecting non-anticipativity in quick-start unit status decision … Read more

Barzilai-Borwein-like rules in proximal gradient schemes for ℓ1−regularized problems

We propose a novel steplength selection rule in proximal gradient methods for minimizing the sum of a differentiable function plus an ℓ1-norm penalty term. The proposed rule modifies one of the classical Barzilai-Borwein steplength, extending analogous results obtained in the context of gradient projection methods for constrained optimization. We analyze the spectral properties of the … Read more

A Semismooth Conjugate Gradients Method — Theoretical Analysis

In large scale applications, deterministic and stochastic variants of Cauchy’s steepest descent method are widely used for the minimization of objectives that are only piecewise smooth. In this paper we analyse a  deterministic descent method based on the generalization of rescaled conjugate gradients proposed by Philip Wolfe in 1975 for objectives that are convex. Without … Read more