In this work we propose and test a new linearisation technique for Binary Quadratic Problems (BQP). We computationally prove that the new formulation, called Extended Linear Formulation, performs much better than the standard one in practice, despite not being stronger in terms of Linear Programming relaxation (LP). We empirically prove that this behaviour is due … Read more
The paper studies stochastic optimization (programming) problems with compound functions containing expectations and extreme values of other random functions as arguments. Compound functions arise in various applications. A typical example is a variance function of nonlinear outcomes. Other examples include stochastic minimax problems, econometric models with latent variables, and multilevel and multicriteria stochastic optimization problems. … Read more
We study mixed integer conic sets involving a general regular (closed, convex, full dimensional, and pointed) cone K such as the nonnegative orthant, the Lorentz cone or the positive semidefinite cone. In a unified framework, we introduce K-minimal inequalities and show that under mild assumptions, these inequalities together with the trivial cone-implied inequalities are sufficient … Read more
We study a class of two-stage stochastic integer programs with general integer variables in both stages and finitely many realizations of the uncertain parameters. Based on Benders’ method, we propose a decomposition algorithm that utilizes Gomory cuts in both stages. The Gomory cuts for the second-stage scenario subproblems are parameterized by the first-stage decision variables, … Read more
In constraining iterative processes, the algorithmic operator of the iterative process is pre-multiplied by a constraining operator at each iterative step. This enables the constrained algorithm, besides solving the original problem, also to find a solution that incorporates some prior knowledge about the solution. This approach has been useful in image restoration and other image … Read more
This paper concerns the method of selecting the best subset of explanatory variables in a multiple linear regression model. To evaluate a subset regression model, some goodness-of-fit measures, e.g., adjusted R^2, AIC and BIC, are generally employed. Although variable selection is usually handled via a stepwise regression method, the method does not always provide the … Read more
In this paper we propose a randomized block coordinate non-monotone gradient (RBCNMG) method for minimizing the sum of a smooth (possibly nonconvex) function and a block-separable (possibly nonconvex nonsmooth) function. At each iteration, this method randomly picks a block according to any prescribed probability distribution and typically solves several associated proximal subproblems that usually have … Read more
In the surface mining industry, the Equipment Selection Problem involves choosing an appropriate fleet of trucks and loaders such that the long-term mine plan can be satisfied. An important characteristic for multi-location (multi-location and multi-dumpsite) mines is that the underlying problem is a multi-commodity flow problem. The problem is therefore at least as difficult as … Read more
In this paper a robust second-order method is developed for the solution of strongly convex l1-regularized problems. The main aim is to make the proposed method as inexpensive as possible, while even difficult problems can be efficiently solved. The proposed method is a primal-dual Newton Conjugate Gradients (pdNCG) method. Convergence properties of pdNCG are studied … Read more
The perceptron algorithm is a simple iterative procedure for finding a point in a convex cone $F$. At each iteration, the algorithm only involves a query of a separation oracle for $F$ and a simple update on a trial solution. The perceptron algorithm is guaranteed to find a feasible point in $F$ after $\Oh(1/\tau_F^2)$ iterations, … Read more