Repository – Page 928 – Optimization Online

Constrained optimization in seismic reflection tomography: an SQP augmented Lagrangian approach

Published: 2004/07/07

Applications - Science and Engineering, Constrained Nonlinear Optimization, Quadratic Programming a priori information, augmented lagrangian method, constrained optimization, least-squares approach, ray tracing, seismic reflection tomography, sequential quadratic programming

Seismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on geological interfaces. From an optimization viewpoint, the problem consists in minimizing a nonlinear least-squares function measuring the mismatch between observed traveltimes and those calculated by ray tracing in this model. The introduction of a priori … Read more

A direct formulation for sparse PCA using semidefinite programming

Published: 2004/07/07

Finance and Economics, Semi-definite Programming, Statistics pca, semidefinite programming, sparsity

We examine the problem of approximating, in the Frobenius-norm sense, a positive, semidefinite symmetric matrix by a rank-one matrix, with an upper bound on the cardinality of its eigenvector. The problem arises in the decomposition of a covariance matrix into sparse factors, and has wide applications ranging from biology to finance. We use a modification … Read more

Fuzzy Modeling with Adaptive Simulated Annealing

Published: 2004/07/05, Updated: 2004/12/13

Hime Aguiar e Oliveira Jr.

Control Applications, Global Optimization Applications

A new method for data-based fuzzy system modeling is presented. The approach uses Takagi-Sugeno models and Adaptive Simulated Annealing (ASA) to achieve its goal . The problem to solve is well defined – given a training set containing a finite number of input-output pairs, construct a fuzzy system that approximates the behavior of the real … Read more

Robust Capacity Expansion of Transit Networks

Published: 2004/07/05

Network Optimization, Robust Optimization, Transportation network planning, robust optimization

In this paper we present a methodology to decide capacity expansions for a transit network that finds a robust solution with respect to the uncertainty in demands and travel times. We show that solving for a robust solution is a computationally tractable problem under conditions that are reasonable for a transportation system. For example, the … Read more

Invariance and efficiency of convex representations

Published: 2004/06/29

Convex Optimization, Linear, Cone and Semidefinite Programming central path, convex optimization, duality, homogeneous cones, interior point methods, semidefinite programming, semidefinite representations, strict complementarity, weighted central path

We consider two notions for the representations of convex cones: $G$-representation and lifted-$G$-representation. The former represents a convex cone as a slice of another; the latter allows in addition, the usage of auxiliary variables in the representation. We first study the basic properties of these representations. We show that some basic properties of convex cones … Read more

Optimizing Preventive Maintenance Models

Published: 2004/06/29

Global Optimization Applications, Scheduling

We deal with the problem of scheduling preventive maintenance (PM) by minimizing a performance function which reflects repair and replacement costs as well as the costs of the PM itself. It is assumed that there is a known model which predicts the frequency of system failure as a function of its age; and it is … Read more

Solving Multistage Asset Investment Problems by the Sample Average Approximation Method

Published: 2004/06/28, Updated: 2005/06/27

Finance and Economics, Stochastic Programming

The vast size of real world stochastic programming instances requires sampling to make them practically solvable. In this paper we extend the understanding of how sampling affects the solution quality of multistage stochastic programming problems. We present a new heuristic for determining good feasible solutions for a multistage decision problem. For power and log-utility functions … Read more

A Global Optimization Problem in Portfolio Selection

Published: 2004/06/25

Finance and Economics, Global Optimization Applications

This paper deals with the issue of buy-in thresholds in portfolio optimization using the Markowitz approach. Optimal values of invested fractions calculated using, for instance, the classical minimum-risk problem can be unsatisfactory in practice because they imply that very small amounts of certain assets are purchased. Realistically, we want to impose a disjoint restriction so … Read more

Solving the Vehicle Routing Problem with Stochastic Demands using the Cross Entropy Method

Published: 2004/06/24

Applications - OR and Management Sciences, Global Optimization cross-entropy method, stochastic optimization, vehicle routing

An alternate formulation of the classical vehicle routing problem with stochastic demands (VRPSD)is considered. We propose a new heuristic method to solve the problem. The algorithm is a modified version of the so-called Cross-Entropy method, which has been proposed in the literature as a heuristics for deterministic combinatorial optimization problems based upon concepts of rare-event … Read more

Variational Analysis of Functions of the Roots of Polynomials

Published: 2004/06/24, Updated: 2004/07/28

Nonsmooth Optimization nonsmooth analysis, subdifferential, subgradient

The Gauss-Lucas Theorem on the roots of polynomials nicely simplifies calculating the subderivative and regular subdifferential of the abscissa mapping on polynomials (the maximum of the real parts of the roots). This paper extends this approach to more general functions of the roots. By combining the Gauss-Lucas methodology with an analysis of the splitting behavior … Read more