A Unifying Framework for the Convexification of Mixed-Integer Conic Binary Sets The paper “Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications,” by Fatma Kilinc-Karzan, Simge Kucukyavuz, Dabeen Lee, Soroosh Shafieezadeh-Abadeh, develops a unifying framework convexifying mixed-integer conic binary sets. Many applications in machine-learning operations research give rise to in...

Abstract: This paper proposes a new algorithm for solving Mixed-Integer Quadratic Programming (MIQP) problems. The algorithm is particularly tailored to solving small-scale MIQPs such as those that arise in embedded hybrid Model Predictive Control (MPC) applications. The approach combines branch and bound (B&B) with nonnegative least squares (NNLS), that are used to solve Quadratic Programming ...

Laurent and Poljak introduced a very general class of valid linear inequalities, called gap inequalities, for the max-cut problem. We show that an analogous class of inequalities can be defined for general nonconvex mixed-integer quadratic programs. These inequalities dominate some inequalities arising from a natural semidefinite relaxation.

Optimization problems involving two decision makers at two different decision levels are referred to as bilevel programming problems. In this work, we present a novel algorithm for the exact and global solution of two classes of bi-level programming problems, namely (i) bi-level mixed-integer linear programming problems (B-MILP) and (ii) bi-level mixed-integer quadratic programming problems (B-...

This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal information functions across pools and within each content area...

In this paper we consider the use of extended formulations in LP-based algorithms for mixed integer conic quadratic programming (MICQP). Through an homogenization procedure we generalize an existing extended formulation to general conic quadratic constraints. We then compare its effectiveness against traditional and extended formulation-based algorithms for MICQP. We find that this new extended...

This paper proposes an original Model Predictive Control approach to the walking control for humanoid robots, which allows to generate stable walking motions without the prior definition of footsteps positions and instants. Both the instant and amplitude of the changes in the supporting surface are part of the walking motion generation problem, and are described by a set of highly-constrained i...

We present semidefinite relaxations for unconstrained nonconvex quadratic mixed-integer optimization problems. These relaxations yield tight bounds and are computationally easy to solve for mediumsized instances, even if some of the variables are integer and unbounded. In this case, the problem contains an infinite number of linear constraints; these constraints are separated dynamically. We us...

e-mail: [email protected] Abstract. The purpose of this paper is threefold. First we propose splitting schemes for reformulating non-separable problems as block-separable problems. Second we show that the Lagrangian dual of a block-separable mixed-integer all-quadratic program (MIQQP) can be formulated as an eigenvalue optimization problem keeping the block-separable structure. Finall...