Ships play the major role in bulk transportation and they need their special energy system. This paper proposes a stochastic programing method for optimal sizing of a hybrid ship power system with energy storage system (ESS), photovoltaic power (PV) and diesel generator. To account for uncertainties, in this study a two-stage stochastic mixed-integer non-linear programing is used to model the o...

It is well known that semidefinite programming (SDP) can be used to derive useful relaxations for a variety of optimisation problems. Moreover, in the particular case of mixed-integer quadratic programs, SDP has been used to reformulate problems, rather than merely relax them. The purpose of reformulation is to strengthen the continuous relaxation of the problem, while leaving the optimal solut...

We propose a modified sequential quadratic programming (SQP) method for solving mixed-integer nonlinear programming problems. 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 stabilized by a tru...

This paper introduces the Global Mixed-Integer Quadratic Optimizer, GloMIQO, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs (MIQCQP) to ε-global optimality. The algorithmic components are presented for: reformulating user input, detecting special structure including convexity and edge-concavity, generating tight convex relaxations, partitioning the sear...

The technique of semidefinite programming (SDP) relaxation can be used to obtain a nontrivial bound on the optimal value of a nonconvex quadratically constrained quadratic program (QCQP). We explore concave quadratic inequalities that hold for any vector in the integer lattice Z, and show that adding these inequalities to a mixed-integer nonconvex QCQP can improve the SDP-based bound on the opt...