In this paper we go one step further in the automatic generation of FPTASes for multi-stage stochastic dynamic programs with scalar state and action spaces, in where the cost-to-go functions have a monotone structure in the state variable. While there exist a few frameworks for automatic generation of FPTASes, so far none of them is … Read more
An important aspect of optimization algorithms, for instance evolutionary algorithms, are termination criteria that measure the proximity of the found solution to the optimal solution set. A frequently used approach is the numerical verification of necessary optimality conditions such as the Karush-Kuhn-Tucker (KKT) conditions. In this paper, we present a proximity measure which characterizes the … Read more
A real symmetric matrix “A” is copositive if the inner product if Ax and x is nonnegative for all x in the nonnegative orthant. Copositive programming has attracted a lot of attention since Burer showed that hard nonconvex problems can be formulated as completely-positive programs. Alas, the power of copositive programming is offset by its … Read more
This paper presents a novel trust-region method for the optimization of multiple expensive functions. We apply this method to a biobjective optimization problem in fluid mechanics, the optimal mixing of particles in a flow in a closed container. The three-dimensional time-dependent flows are driven by Lorentz forces that are generated by an oscillating permanent magnet … Read more
This paper develops a novel limited-memory method to solve dynamic optimization problems. The memory requirements for such problems often present a major obstacle, particularly for problems with PDE constraints such as optimal flow control, full waveform inversion, and optical tomography. In these problems, PDE constraints uniquely determine the state of a physical system for a … Read more
This paper presents a novel price setting optimization problem for an energy retailer in the smart grid. In this framework the retailer buys energy from multiple generators via bilateral contracts, and sells it to a population of smart homes using Time-and-Level-of-Use prices (TLOU). TLOU is an energy price structure recently introduced in the literature, where … Read more
Efficiently handling last-mile deliveries becomes more and more important nowadays. Using drones to support classical vehicles allows improving delivery schedules as long as efficient solution methods to plan last-mile deliveries with drones are available. We study exact solution approaches for some variants of the traveling salesman problem with drone (TSP-D) in which a truck and … Read more
We study a class of single-objective nonlinear optimization problems, the so-called Integer Linear Generalized Maximum Multiplicative Programs (IL-GMMP). This class of optimization problems has a significant number of applications in different fields of study including but not limited to game theory, systems reliability, and conservative planning. An IL-GMMP can be reformulated as a mixed integer … Read more
The paper overviews stochastic optimization models of insurance mathematics and methods for their solution from the point of view of stochastic programming and stochastic optimal control methodology, with vector optimality criteria. The evolution of an insurance company’s capital is considered in discrete time. The main random variables, which influence this evolution, are levels of payments, … Read more
We introduce an iterative method named BiLQ for solving general square linear systems Ax = b based on the Lanczos biorthogonalization process defined by least-norm subproblems, and is a natural companion to BiCG and QMR. Whereas the BiCG (Fletcher, 1976), CGS (Sonneveld, 1989) and BiCGSTAB (van der Vorst, 1992) iterates may not exist when the … Read more