Approximate linear programs (ALPs) are well-known models for computing value function approximations (VFAs) of intractable Markov decision processes (MDPs) arising in applications. VFAs from ALPs have desirable theoretical properties, define an operating policy, and provide a lower bound on the optimal policy cost, which can be used to assess the suboptimality of heuristic policies. However, … Read more
In this paper we extend naturally the scalarization proximal point method to solve multiobjective unconstrained minimization problems, proposed by Apolinario et al.(2016), from Euclidean spaces to Hadamard manifolds for locally Lipschitz and quasiconvex vector objective functions. Moreover, we present a convergence analysis, under some mild assumptions on the multiobjective function, for two inexact variants of … Read more
Consider settings such as stochastic optimization where a smooth objective function $f$ is unknown but can be estimated with an \emph{inexact oracle} such as quasi-Monte Carlo (QMC) or numerical quadrature. The inexact oracle is assumed to yield function estimates having error that decays with increasing oracle effort. For solving such problems, we present the Adaptive … Read more
We study the problem of choosing the best subset of p features in linear regression given n observations. This problem naturally contains two objective functions including minimizing the amount of bias and minimizing the number of predictors. The existing approaches transform the problem into a single-objective optimization problem either by combining the two objectives using … Read more
We consider convex optimization problems formulated using dynamic programming equations. Such problems can be solved using the Dual Dynamic Programming algorithm combined with the Level 1 cut selection strategy or the Territory algorithm to select the most relevant Benders cuts. We propose a limited memory variant of Level 1 and show the convergence of DDP … Read more
We study the computational complexity of the infinite-horizon discounted-reward Markov Decision Problem (MDP) with a finite state space $\cS$ and a finite action space $\cA$. We show that any randomized algorithm needs a running time at least $\Omega(\carS^2\carA)$ to compute an $\epsilon$-optimal policy with high probability. We consider two variants of the MDP where the … Read more
In this paper we present a four-level market model that accounts for airport capacity extension, fleet investment, aircraft scheduling, and ticket trade in a liberalized aviation market with independent decision makers. In particular, budget-constrained airports decide on the first level on their optimal runway capacity extension and on a corresponding airport charge. Airports anticipate optimal … Read more
This study looks at the application of mathematical concepts of entropy and Fibonacci sequence in creating optimal dimensional relations of classification character. The paper is devoted to optimization of some numerical relations and integers as unified threshold characteristics of classification type, aimed for example at systemic optimizing the measuring information of various processes. The paper … Read more
In this paper, we follow Kuroiwa’s set approach in set optimization, which proposes to compare values of a set-valued objective map $F$ respect to various set order relations. We introduce a Hausdorff-type distance relative to an ordering cone between two sets in a Banach space and use it to define a directional derivative for $F$. … Read more
Bilevel problems model instances with a hierarchical structure. Aiming at an efficient solution of a constrained multiobjective problem according with some pre-defined criterion, we reformulate this optimization but non standard problem as a classic bilevel one. This reformulation intents to encompass all the objectives, so that the properly efficient solution set is recovered by means … Read more