Search results for "Mathematical optimization"

Approximations and Metric Regularity in Mathematical Programming in Banach Space

1993

This paper establishes verifiable conditions ensuring the important notion of metric regularity for general nondifferentiable programming problems in Banach spaces. These conditions are used to obtain Lagrange-Kuhn-Tucker multipliers for minimization problems with infinitely many inequality and equality constraints.

A Nondifferentiable Optimization Approach to Ratio-Cut Partitioning

2003

We propose a new method for finding the minimum ratio-cut of a graph. Ratio-cut is NP-hard problem for which the best previously known algorithm gives an O(log n)-factor approximation by solving its dually related maximum concurrent flow problem.We formulate the minimum ratio-cut as a certain nondifferentiable optimization problem, and show that the global minimum of the optimization problem is equal to the minimum ratio-cut. Moreover, we provide strong symbolic computation based evidence that any strict local minimum gives an approximation by a factor of 2. We also give an efficient heuristic algorithm for finding a local minimum of the proposed optimization problem based on standard nondi…

An improved iterative nonlinear least square approximation method for the design of measurement-based wideband mobile radio channel simulators

2011

This paper deals with the design of measurement-based simulation models for wideband single-input single-output (SISO) mobile radio channels. We present an improved version of the iterative nonlinear least square approximation (INLSA) method for computing the parameters of measurement-based simulation models. The proposed method aims to fit the temporal-frequency correlation function (TFCF) of the simulation model to that of the measured channel. Unlike the original INLSA method, the proposed approach provides a unique optimal set of estimated model parameters. The proposed iterative procedure involves numerical optimization techniques to determine a set of parameters that minimizes the Euc…

Mixed integer optimal compensation: Decompositions and mean-field approximations

2012

Mixed integer optimal compensation deals with optimizing integer- and real-valued control variables to compensate disturbances in dynamic systems. The mixed integer nature of controls might be a cause of intractability for instances of larger dimensions. To tackle this issue, we propose a decomposition method which turns the original n-dimensional problem into n independent scalar problems of lot sizing form. Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon. This last reformulation step mirrors a standard procedure in mixed integer programming. We apply the decomposition method to a mean-field coupled multi-agent s…

2014

This paper deals with the problem of robust model predictive control (RMPC) for a class of linear time-varying systems with constraints and data losses. We take the polytopic uncertainties into account to describe the uncertain systems. First, we design a robust state observer by using the linear matrix inequality (LMI) constraints so that the original system state can be tracked. Second, the MPC gain is calculated by minimizing the upper bound of infinite horizon robust performance objective in terms of linear matrix inequality conditions. The method of robust MPC and state observer design is illustrated by a numerical example.

Multi-Objective and Multi-Criteria Analysis for Optimal Pump Scheduling in Water Systems

2018

This contribution focuses on the problem of optimal pump scheduling, a fundamental element in pursuing operation optimization of water distribution systems. A combined approach of multi-objective optimization and multi-criteria analysis is herein suggested to first find the Pareto front of non-dominated solutions and then to rank them based on a set of weighted criteria. The Non-Dominated Sorting Genetic Algorithm (NSGA-II) is proposed to solve the multi-objective problem, while the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is used to achieve the final ranking.

Response determination of linear dynamical systems with singular matrices: A polynomial matrix theory approach

2017

Abstract An approach is developed based on polynomial matrix theory for formulating the equations of motion and for determining the response of multi-degree-of-freedom (MDOF) linear dynamical systems with singular matrices and subject to linear constraints. This system modeling may appear for reasons such as utilizing redundant DOFs, and can be advantageous from a computational cost perspective, especially for complex (multi-body) systems. The herein developed approach can be construed as an alternative to the recently proposed methodology by Udwadia and coworkers, and has the significant advantage that it circumvents the use of pseudoinverses in determining the system response. In fact, ba…

SMAA in Robustness Analysis

2016

Stochastic multicriteria acceptability analysis (SMAA) is a simulation based method for discrete multicriteria decision aiding problems where information is uncertain, imprecise, or partially missing. In SMAA, different kind of uncertain information is represented by probability distributions. Because SMAA considers simultaneously the uncertainty in all parameters, it is particularly useful for robustness analysis. Depending on the problem setting, SMAA determines all possible rankings or classifications for the alternatives, and quantifies the possible results in terms of probabilities. This chapter describes SMAA in robustness analysis using a real-life decision problem as an example. Bas…

On Generalizing Lipschitz Global Methods forMultiobjective Optimization

2015

Lipschitz global methods for single-objective optimization can represent the optimal solutions with desired accuracy. In this paper, we highlight some directions on how the Lipschitz global methods can be extended as faithfully as possible to multiobjective optimization problems. In particular, we present a multiobjective version of the Pijavskiǐ-Schubert algorithm.

NIMBUS — Interactive Method for Nondifferentiable Multiobjective Optimization Problems

1996

An interactive method, NIMBUS, for nondifferentiable multiobjective optimization problems is introduced. We assume that every objective function is to be minimized The idea of NIMBUS is that the decision maker can easily indicate what kind of improvements are desired and what kind of impairments are tolerable at the point considered.