Uplift Quadratic Program in Irish Electricity Price Setting

Bord Gis required a deeper insight into the dynamics of Uplift prices. The aim of the group was to apply a variety of analytical tools to the problem in order to satisfy Bord Gis requirements. The group conducted a KKT Optimality Analysis of the quadratic program used to determine the Uplift prices, performed statistical analysis to identify the binding constraints and their sensitives to the Uplift prices, simulated a synthetic stochastic process that is consistent with the Uplift pricing series and investigated alternative objective functions for the quadratic program

Immunizing Conic Quadratic Optimization Problems Against Implementation Errors

We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonalized. This extension of the S-lemma may also be useful for other purposes. We extend the result to the case in which the uncertainty region is the intersection of two convex quadratic inequalities. The robust counterpart for this case is also equivalent to a system of conic quadratic constraints. Results for convex conic quadratic constraints with implementation error are also given. We conclude with showing how the theory developed can be applied in robust linear optimization with jointly uncertain parameters and implementation errors, in sequential robust quadratic programming, in Taguchi’s robust approach, and in the adjustable robust counterpart.Conic Quadratic Program;hidden convexity;implementation error;robust optimization;simultaneous diagonalizability;S-lemma

Solving Quadratic Equations via PhaseLift when There Are About As Many Equations As Unknowns

This note shows that we can recover a complex vector x in C^n exactly from on the order of n quadratic equations of the form ||^2 = b_i, i = 1, ..., m, by using a semidefinite program known as PhaseLift. This improves upon earlier bounds in [3], which required the number of equations to be at least on the order of n log n. We also demonstrate optimal recovery results from noisy quadratic measurements; these results are much sharper than previously known results.Comment: 6 page

Unbounded convex sets for non-convex mixed-integer quadratic programming

This paper introduces a fundamental family of unbounded convex sets that arises in the context of non-convex mixed-integer quadratic programming. It is shown that any mixed-integer quadratic program with linear constraints can be reduced to the minimisation of a linear function over a face of a set in the family. Some fundamental properties of the convex sets are derived, along with connections to some other well-studied convex sets. Several classes of valid and facet-inducing inequalities are also derived

An Efficiently Solvable Quadratic Program for Stabilizing Dynamic Locomotion

We describe a whole-body dynamic walking controller implemented as a convex quadratic program. The controller solves an optimal control problem using an approximate value function derived from a simple walking model while respecting the dynamic, input, and contact constraints of the full robot dynamics. By exploiting sparsity and temporal structure in the optimization with a custom active-set algorithm, we surpass the performance of the best available off-the-shelf solvers and achieve 1kHz control rates for a 34-DOF humanoid. We describe applications to balancing and walking tasks using the simulated Atlas robot in the DARPA Virtual Robotics Challenge.Comment: 6 pages, published at ICRA 201