In this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for bounded random variables known as the forward and backward deviations. These deviation measures capture distributional asymmetry and lead to better approximations of chance constraints. We also propose a tractable robust optimization approach for obtaining robust solutions … Read more
The paper continues investigations of stationarity and regularity properties of set systems in normed spaces started in the previous paper of the author. It contains a summary of different characterizations (both primal and dual) of regularity and a list of sufficient conditions for a set system to be regular. Citation University of Ballarat, School of … Read more
Non-Linear Stochastic Fractional programming models provide numerous insights into a wide variety of areas such as in financial derivatives. Portfolio optimization has been one of the important research fields in modern finance. The most important character within this optimization problem is the uncertainty of the future returns on assets. The objective of this study is … Read more
Medical Physics — January 2006 — Volume 33, Issue 1, pp. 225-234. Citation Medical Physics — January 2006 — Volume 33, Issue 1, pp. 225-234.
We propose minimum volume ellipsoids (MVE) clustering as an alternate clustering technique to k-means clustering for Gaussian data points and explore its value and practicality. MVE clustering allocates data points into clusters that minimizes the total volumes of each cluster’s covering ellipsoids. Motivations for this approach include its scale-invariance, its ability to handle asymmetric and … Read more
Fractional programming deals with the optimization of one or several ratios of functions subject to constraints. Most of these optimization problems are not convex while some of them are still generalised convex. After about forty years of research, well over one thousand articles have appeared on applications, theory and solution methods for various types of … Read more
We present a general theory for transforming a homogeneous conic system F: Ax = 0, x \in C, x \ne 0, to an equivalent system via projective transformation induced by the choice of a point in a related dual set. Such a projective transformation serves to pre-condition the conic system into a system that has … Read more
In our reports on GAMM-04 and ECCOMAS-04 there has been presented a new conjugate directions method for large scale unconstrained minimization problems. High efficiency of this method is ensured by employing an orthogonalization procedure: when constructing the next conjugate vector the component of the gradient is used that is orthogonal to the subspace of preceding … Read more
This paper is concerned with the application of semidefinite programming to the satisfiability problem, and in particular with using semidefinite liftings to efficiently obtain proofs of unsatisfiability. We focus on the Tseitin satisfiability instances which are known to be hard for many proof systems. We present an explicit semidefinite programming problem with dimension linear in … Read more
We propose two line search primal-dual interior-point methods that approximately solve a equence of equality constrained barrier subproblems. To solve each subproblem, our methods apply a modified Newton method and use an $\ell_2$-exact penalty function to attain feasibility. Our methods have strong global convergence properties under standard assumptions. Specifically, if the penalty parameter remains bounded, … Read more