A Smoothing SQP Framework for a Class of Composite $ Minimization over Polyhedron
The composite $L_q$ (0
New symmetries in mixed-integer linear optimization
We present two novel applications of symmetries for mixed-integer linear programming. First we propose two variants of a new heuristic to improve the objective value of a feasible solution using symmetries. These heuristics can use either the actual permutations or the orbits of the variables to find better feasible solutions. Then we introduce a new … Read more
Robust Block Coordinate Descent
In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly nonseparable or ill conditioned problems. We call the method Robust Coordinate Descent (RCD). At … Read more
The Principle of Hamilton for Mechanical Systems with Impacts and Unilateral Constraints
An action integral is presented for Hamiltonian mechanics in canonical form with unilateral constraints and/or impacts. The transition conditions on generalized impulses and the energy are presented as variational inequalities, which are obtained by the application of discontinuous transversality conditions. The energetical behavior for elastic, plastic and blocking type impacts are analyzed. A general impact … Read more
Cut Generation for Optimization Problems with Multivariate Risk Constraints
We consider a class of multicriteria stochastic optimization problems that features benchmarking constraints based on conditional value-at-risk and second-order stochastic dominance. We develop alternative mixed-integer programming formulations and solution methods for cut generation problems arising in optimization under such multivariate risk constraints. We give the complete linear description of two non-convex substructures appearing in these … Read more
Formal property verification in a conformance testing framework
In model-based design of cyber-physical systems, such as switched mixed-signal circuits or software-controlled physical systems, it is common to develop a sequence of system models of different fidelity and complexity, each appropriate for a particular design or verification task. In such a sequence, one model is often derived from the other by a process of … Read more
Hypotheses testing on the optimal values of several risk-neutral or risk-averse convex stochastic programs and application to hypotheses testing on several risk measure values
Given an arbitrary number of risk-averse or risk-neutral convex stochastic programs, we study hypotheses testing problems aiming at comparing the optimal values of these stochastic programs on the basis of samples of the underlying random vectors. We propose non-asymptotic tests based on confidence intervals on the optimal values of the stochastic programs obtained using the … Read more
Beyond the Birkhoff Polytope: Convex Relaxations for Vector Permutation Problems
The Birkhoff polytope (the convex hull of the set of permutation matrices) is frequently invoked in formulating relaxations of optimization problems over permutations. The Birkhoff polytope is represented using Θ(n^2) variables and constraints, significantly more than the n variables one could use to represent a permutation as a vector. Using a recent construction of Goemans … Read more
Projection methods in quantum information science
We consider the problem of constructing quantum operations or channels, if they exist, that transform a given set of quantum states $\{\rho_1, \dots, \rho_k\}$ to another such set $\{\hat\rho_1, \dots, \hat\rho_k\}$. In other words, we must find a {\em completely positive linear map}, if it exists, that maps a given set of density matrices to … Read more
A Feasible Active Set Method with Reoptimization for Convex Quadratic Mixed-Integer Programming
We propose a feasible active set method for convex quadratic programming problems with non-negativity constraints. This method is specifically designed to be embedded into a branch-and-bound algorithm for convex quadratic mixed integer programming problems. The branch-and-bound algorithm generalizes the approach for unconstrained convex quadratic integer programming proposed by Buchheim, Caprara and Lodi to the presence … Read more