150 research outputs found
Matrix Minor Reformulation and SOCP-based Spatial Branch-and-Cut Method for the AC Optimal Power Flow Problem
Alternating current optimal power flow (AC OPF) is one of the most
fundamental optimization problems in electrical power systems. It can be
formulated as a semidefinite program (SDP) with rank constraints. Solving AC
OPF, that is, obtaining near optimal primal solutions as well as high quality
dual bounds for this non-convex program, presents a major computational
challenge to today's power industry for the real-time operation of large-scale
power grids. In this paper, we propose a new technique for reformulation of the
rank constraints using both principal and non-principal 2-by-2 minors of the
involved Hermitian matrix variable and characterize all such minors into three
types. We show the equivalence of these minor constraints to the physical
constraints of voltage angle differences summing to zero over three- and
four-cycles in the power network. We study second-order conic programming
(SOCP) relaxations of this minor reformulation and propose strong cutting
planes, convex envelopes, and bound tightening techniques to strengthen the
resulting SOCP relaxations. We then propose an SOCP-based spatial
branch-and-cut method to obtain the global optimum of AC OPF. Extensive
computational experiments show that the proposed algorithm significantly
outperforms the state-of-the-art SDP-based OPF solver and on a simple personal
computer is able to obtain on average a 0.71% optimality gap in no more than
720 seconds for the most challenging power system instances in the literature
Extended Formulations in Mixed-integer Convex Programming
We present a unifying framework for generating extended formulations for the
polyhedral outer approximations used in algorithms for mixed-integer convex
programming (MICP). Extended formulations lead to fewer iterations of outer
approximation algorithms and generally faster solution times. First, we observe
that all MICP instances from the MINLPLIB2 benchmark library are conic
representable with standard symmetric and nonsymmetric cones. Conic
reformulations are shown to be effective extended formulations themselves
because they encode separability structure. For mixed-integer
conic-representable problems, we provide the first outer approximation
algorithm with finite-time convergence guarantees, opening a path for the use
of conic solvers for continuous relaxations. We then connect the popular
modeling framework of disciplined convex programming (DCP) to the existence of
extended formulations independent of conic representability. We present
evidence that our approach can yield significant gains in practice, with the
solution of a number of open instances from the MINLPLIB2 benchmark library.Comment: To be presented at IPCO 201
MINLP model for work and heat exchange networks synthesis considering unclassified streams
The optimal synthesis of work and heat exchange networks (WHENs) is deeply important to achieve simultaneously high energy efficiency and low costs in chemical processes via work and heat integration of process streams. This paper presents an efficient MINLP model for optimal WHENs synthesis derived from a superstructure that considers unclassified streams. The derived model is solved using BARON global optimization solver. The superstructure considers multi-staged heat integration with isothermal mixing, temperature adjustment with hot or cold utility, and work exchange network for streams that are not classified a priori. The leading advantage of the present optimization model is the capability of defining the temperature and pressure route, i.e. heating up, cooling down, expanding, or compressing, of a process stream entirely during optimization while still being eligible for global optimization. The present approach is tested to a small-scale WHEN problem and the result surpassed the ones from the literature.The authors LFS, CBBC, and MASSR acknowledge the National Council for Scientific and Technological Development – CNPq (Brazil), processes 148184/2019-7, 440047/2019-6, 311807/2018-6, 428650/2018-0, and Coordination for the Improvement of Higher Education Personnel – CAPES (Brazil) for the financial support. The author JAC acknowledge financial support from the “Generalitat Valenciana” under project PROMETEO 2020/064
Nonlinear model predictive control based on Bernstein global optimization with application to a nonlinear CSTR
© 2016 EUCA. We present a model predictive control based tracking problem for nonlinear systems based on global optimization. Specifically, we introduce a 'Bernstein global optimization' procedure and demonstrate its applicability to the aforementioned control problem. This Bernstein global optimization procedure is applied to predictive control of a nonlinear CSTR system. Its strength and benefits are compared with those of a sub-optimal procedure, as implemented in MATLAB using fmincon function, and two well established global optimization procedures, BARON and BMIBNB.National Research Foundation, Singapore
A Polynomial Optimization Approach to Constant Rebalanced Portfolio Selection
We address the multi-period portfolio optimization problem with the constant rebalancing strategy. This problem is formulated as a polynomial optimization problem (POP) by using a mean-variance criterion. In order to solve the POPs of high degree, we develop a cutting-plane algorithm based on semidefinite programming. Our algorithm can solve problems that can not be handled by any of known polynomial optimization solvers.Multi-period portfolio optimization;Polynomial optimization problem;Constant rebalancing;Semidefinite programming;Mean-variance criterion
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