This paper overviews the development of a framework for the optimization of black-box mixed-integer functions subject to bound constraints. Our methodology is based on the use of tailored surrogate approximations of t...
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This paper overviews the development of a framework for the optimization of black-box mixed-integer functions subject to bound constraints. Our methodology is based on the use of tailored surrogate approximations of the unknown objective function, in combination with a trust-region method. To construct suitable model approximations, we assume that the unknown objective is locally quadratic, and we prove that this leads to fully-linear models in restricted discrete neighborhoods. We show that the proposed algorithm converges to a first-order mixed-integer stationary point according to several natural definitions of mixed-integer stationarity, depending on the structure of the objective function. We present numerical results to illustrate the computational performance of different implementations of this methodology in comparison with the state-of-the-art derivative-free solver NOMAD.
This letter proposes a structure-aware automatic differentiation method to accelerate the solution of alternating current optimal power flow (ACOPF) with nonlinear programming (NLP) solvers. By exploiting the isomorph...
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This letter proposes a structure-aware automatic differentiation method to accelerate the solution of alternating current optimal power flow (ACOPF) with nonlinear programming (NLP) solvers. By exploiting the isomorphic structure of nonlinear power flow constraints in ACOPF, specialized binary code is generated to efficiently compute the Jacobian and Hessian matrix. Numerical tests show that our implementation achieves over 18% speedup in the total solution process and 40% speedup in automatic differentiation for large-scale ACOPF problems compared to state-of-the-art algebraic modeling languages of NLP.
The solution of nonconvex parameter estimation problems with deterministic global optimization methods is desirable but challenging, especially if large measurement datasets are considered. We propose to exploit the s...
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The solution of nonconvex parameter estimation problems with deterministic global optimization methods is desirable but challenging, especially if large measurement datasets are considered. We propose to exploit the structure of this class of optimization problems to enable their solution with the spatial branch -and -bound algorithm. In detail, we start with a reduced dataset in the root node and progressively augment it, converging to the full dataset. We show for nonlinear programs (NLPs) that our algorithm converges to the global solution of the original problem considering the full dataset. The implementation of the algorithm extends our opensource solver MAiNGO. A numerical case study with a mixed -integer nonlinear program (MINLP) from chemical engineering and a dynamic optimization problem from biochemistry both using noise -free measurement data emphasizes the potential for savings of computational effort with our proposed approach.
The interior-point method (IPM) has become the workhorse method for nonlinear programming. The performance of IPM is directly related to the linear solver employed to factorize the Karush-Kuhn-Tucker (KKT) system at e...
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The interior-point method (IPM) has become the workhorse method for nonlinear programming. The performance of IPM is directly related to the linear solver employed to factorize the Karush-Kuhn-Tucker (KKT) system at each iteration of the algorithm. When solving large-scale nonlinear problems, state-of-the art IPM solvers rely on efficient sparse linear solvers to solve the KKT system. Instead, we propose a novel reduced-space IPM algorithm that condenses the KKT system into a dense matrix whose size is proportional to the number of degrees of freedom in the problem. Depending on where the reduction occurs, we derive two variants of the reduced-space method: linearize-then-reduce and reduce-then-linearize. We adapt their workflow so that the vast majority of computations are accelerated on GPUs. We provide extensive numerical results on the optimal power flow problem, comparing our GPU-accelerated reduced-space IPM with Knitro and a hybrid full-space IPM algorithm. By evaluating the derivatives on the GPU and solving the KKT system on the CPU, the hybrid solution is already significantly faster than the CPU-only solutions. The two reduced-space algorithms go one step further by solving the KKT system entirely on the GPU. As expected, the performance of the two reduction algorithms depends critically on the number of available degrees of freedom: They underperform the full-space method when the problem has many degrees of freedom, but the two algorithms are up to three times faster than Knitro as soon as the relative number of degrees of freedom becomes smaller.
Under development since the early 1990s, BARON has become a highly robust and efficient computational system for solving nonconvex continuous and discrete optimization problems to global optimality. This work discusse...
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Under development since the early 1990s, BARON has become a highly robust and efficient computational system for solving nonconvex continuous and discrete optimization problems to global optimality. This work discusses key features that were introduced to BARON in the past decade, including hybrid relaxations, linear and nonlinear presolve methods, enhanced convexification methods, heuristics, and various robustness enhancements. A systematic computational comparison on benchmark libraries is presented among various state-of-the-art local and global codes for nonlinear and mixed-integer nonlinear programs. The results demonstrate the benefits from the newly added algorithmic facilities, and the leading performance of BARON over both local and global solvers.
In this paper, we consider the weighted nonlinear complementarity problem which is the extension of the general complementarity problems and contains a wide class of optimization problems. Based on the weighted comple...
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In this paper, we consider the weighted nonlinear complementarity problem which is the extension of the general complementarity problems and contains a wide class of optimization problems. Based on the weighted complementarity function, we reformulate the weighted nonlinear complementarity problem as an unconstrained minimization problem and present the steepest descent-based neural network to solve it. Under mild conditions, we derive some results related to the asymptotic stability of the neural network. Numerical experiments indicate that the proposed algorithm is quite effective.
We present an online algorithm for time-varying semidefinite programs (TV-SDPs), based on the tracking of the solution trajectory of a low-rank matrix factorization, also known as the Burer-Monteiro factorization, in ...
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We present an online algorithm for time-varying semidefinite programs (TV-SDPs), based on the tracking of the solution trajectory of a low-rank matrix factorization, also known as the Burer-Monteiro factorization, in a path-following procedure. There, a predictor-corrector algorithm solves a sequence of linearized systems. This requires the introduction of a horizontal space constraint to ensure the local injectivity of the low-rank factorization. The method produces a sequence of approximate solutions for the original TV-SDP problem, for which we show that they stay close to the optimal solution path if properly initialized. Numerical experiments for a timevarying max-cut SDP relaxation demonstrate the computational advantages of the proposed method for tracking TV-SDPs in terms of runtime compared to off-the-shelf interior-point methods.
Recently, several works have focused on modeling and simulating the cashew apple juice fermentation process. However, multi-objective optimization (MOO) studies for constructing the Pareto set of this process have not...
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Recently, several works have focused on modeling and simulating the cashew apple juice fermentation process. However, multi-objective optimization (MOO) studies for constructing the Pareto set of this process have not yet been conducted. In this work, the model-based optimization of the fermentation of cashew apple juice was carried out using a MOO strategy based on the weighted sum method (WSM). The Nelder-Mead (NM) algorithm was implemented using Scilab software. In the proposed strategy, three parameters were simultaneously optimized: (i) the ethanol-substrate fed ratio, (ii) the ethanol-substrate consumed ratio and (iii) the volumetric ethanol productivity. The temperature and initial substrate concentration of the cashew juice, as well as the operating time, were used as decision variables. The simulation results were compared to data obtained from recent literature, such that the residual standard deviation (RSD) could be computed for different temperatures and initial concentrations of the substrate, ethanol, and biomass. The maximum value of RSD was 5.26% for the substrate concentration at 30 & DEG;C. The Pareto curve results showed that the process productivity could be adjusted with substrate consumption and that it is a valuable tool to avoid selecting operational points away from the optimal region.
Nonmonotonicity has been considered to be essentially influential on the efficiency of the iterative procedures of nonlinear optimization. A review of the literature shows that the objective function values available ...
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Nonmonotonicity has been considered to be essentially influential on the efficiency of the iterative procedures of nonlinear optimization. A review of the literature shows that the objective function values available from recent iterations provide worthier information in the nonmonotone schemes. So, with the aim of enhancing probability of applying more recent available function values, a nonmonotone trust region ratio is suggested using a forgetting factor. Meanwhile, modification of a recent adaptive formula for the trust region radius is devised by a nonmonotone reflection as well. Then, based on the two mentioned modifications, an adaptive nonmonotone trust region algorithm is given. In addition, convergence of the method is analysed under classic assumptions. To provide support for our theoretical arguments, computational merits of the given algorithm on a set of CUTEr test functions are depicted.
In order to improve the safety performance of 18650 lithium battery in storage and transportation, the thermal runaway expansion research of nine-palace grid glass fiber partition packaging was studied by experiment a...
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In order to improve the safety performance of 18650 lithium battery in storage and transportation, the thermal runaway expansion research of nine-palace grid glass fiber partition packaging was studied by experiment and computational simulation. The results show that the glass fiber partition with a certain gap between the batteries and the partition can effectively inhibit the thermal runaway expansion of lithium battery. The optimal distance between the battery and the partition is 2.2 mm, and the thickness of the partition is 1.2 mm. Under the optimal condition, the highest temperature near the surface of the battery is only about 130. The safety and protection performance of a lithium battery can be significantly improved by using the optimized glass fiber partition packaging.
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