Randomized Block Coordinate Non-Monotone Gradient Method for a Class of Nonlinear Programming

Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , ,

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

Mixed Integer Second-Order Cone Programming Formulations for Variable Selection

Categories (Mixed) Integer Nonlinear Programming, Second-Order Cone Programming, Statistics Tags , , , , ,

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

An MILP approach to Multi-location, Multi-Period Equipment Selection for Surface Mining with Case Studies

Categories Applications - OR and Management Sciences Tags , ,

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

A Second-Order Method for Strongly Convex L1-Regularization Problems

Categories Convex and Nonsmooth Optimization Tags , , , ,

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

A Deterministic Rescaled Perceptron Algorithm

Categories Convex Optimization Tags , ,

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

Robust Optimization of Sums of Piecewise Linear Functions with Application to Inventory Problems

Categories (Mixed) Integer Linear Programming, Production and Logistics, Robust Optimization Tags , , , , , ,

Robust optimization is a methodology that has gained a lot of attention in the recent years. This is mainly due to the simplicity of the modeling process and ease of resolution even for large scale models. Unfortunately, the second property is usually lost when the cost function that needs to be robustified is not concave … Read more

A Robust Formulation of the Uncertain Set Covering Problem

Categories Applications - OR and Management Sciences, Robust Optimization Tags , ,

This work introduces a robust formulation of the uncertain set covering problem combining the concepts of robust and probabilistic optimization. It is shown that the proposed robust uncertain set covering problem can be stated as a compact mixed-integer linear programming model which can be solved with modern computer software. This model is a natural extension … Read more

A new approximation hierarchy for polynomial conic optimization

Categories Linear, Cone and Semidefinite Programming

In this paper we consider polynomial conic optimization problems, where the feasible set is defined by constraints in the form of given polynomial vectors belonging to given nonempty closed convex cones, and we assume that all the feasible solutions are nonnegative. This family of problems captures in particular polynomial optimization problems, polynomial semidefinite polynomial optimization … Read more

A Penalized Quadratic Convex Reformulation Method for Random Quadratic Unconstrained Binary Optimization

Categories 0-1 Programming, Stochastic Approaches Tags , ,

The Quadratic Convex Reformulation (QCR) method is used to solve quadratic unconstrained binary optimization problems. In this method, the semidefinite relaxation is used to reformulate it to a convex binary quadratic program which is solved using mixed integer quadratic programming solvers. We extend this method to random quadratic unconstrained binary optimization problems. We develop a … Read more