This paper addresses the globally optimal solution of the network-constrained unit commitment (NCUC) problem incorporating a nonlinear alternating current (AC) model of the transmission network. We formulate the NCUC as a mixed-integer quadratically constrained quadratic programming (MIQCQP) problem. A global optimization algorithm is developed based on a multi-tree approach that iterates betwe...

The Fortran subroutine MISQP solves mixed-integer nonlinear programming problems by a modified sequential quadratic programming (SQP) method. Under the assumption that integer variables have a smooth influence on the model functions, i.e., that function values do not change drastically when inor decrementing an integer value, successive quadratic approximations are applied. The algorithm is sta...

The Fortran subroutine MISQP solves mixed-integer nonlinear programming problems by a modified sequential quadratic programming (SQP) method. Under the assumption that integer variables have a smooth influence on the model functions, i.e., that function values do not change drastically when inor decrementing an integer value, successive quadratic approximations are applied. The algorithm is sta...

We address the exact solution of general integer quadratic programs with linear constraints. These programs constitute a particular case of mixed-integer quadratic programs for which we introduce in [3] a general solution method based on quadratic convex reformulation, that we called MIQCR. This reformulation consists in designing an equivalent quadratic program with a convex objective function...

Let A be an (m × n) integral matrix, and let P = {x : Ax ≤ b} be an n-dimensional polytope. The width of P is defined as w(P ) = min{x ∈ Z\{0} : maxx∈Pxu−minx∈Pxv}. Let ∆(A) and δ(A) denote the greatest and the smallest absolute values of a determinant among all r(A)× r(A) submatrices of A, where r(A) is the rank of a matrix A. We prove that if every r(A) × r(A) sub-matrix of A has a determinan...

This work addresses the development of an efficient solution strategy for obtaining global optima of continuous, integer, and mixed-integer nonlinear programs. Towards this end, we develop novel relaxation schemes, range reduction tests, and branching strategies which we incorporate into the prototypical branch-and-bound algorithm. In the theoretical/algorithmic part of the paper, we begin by d...

The Perspective Relaxation (PR) is a general approach for constructing tight approximations to Mixed-Integer NonLinear Problems with semicontinuous variables. The PR of a MINLP can be formulated either as a Mixed-Integer Second-Order Cone Program (provided that the original objective function is SOCP-representable), or as a Semi-Infinite MINLP. While these reformulations significantly improve t...

 We consider a generalization of the classical quadratic assignment problem, where coordinates of locations are uncertain and only upper and lower bounds are known for each coordinate. We develop a mixed integer linear programming model as a robust counterpart of the proposed uncertain model. A key challenge is that, since the uncertain model involves nonlinear objective function of the ...