A non-modular building layout is amongst the leading sources of offcut waste, resulting from a substantial amount of onsite cutting and fitting of bricks, blocks, plasterboard, and tiles. The field of design for dimen...
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A non-modular building layout is amongst the leading sources of offcut waste, resulting from a substantial amount of onsite cutting and fitting of bricks, blocks, plasterboard, and tiles. The field of design for dimensional coordination is concerned with finding an optimal configuration for non-overlapping spaces in the layout to reduce materials waste. In this article, we propose a convex optimisation-based algorithm for finding alternative floor layouts to enforce the design for dimensional coordination. At the crux of the proposed algorithm lies two mathematical models. The first is the convex relaxation model that establishes the topology of spaces within the layout through relative positioning constraints. We employed acyclic graphs to generate a minimal set of relative positioning constraints to model the problem. The second model optimises the geometry of spaces based on the modular size. The algorithm exploits aspect ratio constraints to restrict the generation of alternate layouts with huge variations. The algorithm is implemented in the BIMWaste tool for automating the design exploration process. BIMWaste is capable of investigating the degree to which designers consider dimensional coordination. We tested the algorithm over 10 completed building projects to report its suitability and accuracy. The algorithm generates competitive floor layouts for the same client intent that are likely to be tidier and more modular. More importantly, those floor layouts have improved waste performance (i.e., 8.75% less waste) due to a reduced tendency for material cutting and fitting. This study, for the first time, used convex programming for the design optimisation with a focus to reduce construction waste.
We analyze the problem of pricing and hedging contingent claims in a financial market described by a multi-period, discrete-time, finite-state scenario tree using an arbitrage-adjusted Sharpe-ratio criterion. We show ...
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We analyze the problem of pricing and hedging contingent claims in a financial market described by a multi-period, discrete-time, finite-state scenario tree using an arbitrage-adjusted Sharpe-ratio criterion. We show that the writer's and buyer's pricing problems are formulated as conic convex optimization problems which allow to pass to dual problems over martingale measures and yield tighter pricing intervals compared to the interval induced by the usual no-arbitrage price bounds. An extension allowing proportional transaction costs is also given. Numerical experiments using S&P 500 options are given to demonstrate the practical applicability of the pricing scheme. (C) 2008 Elsevier Ltd. All rights reserved.
This paper carries out a comprehensive analysis on an offshore wind farm equipped with a hybrid storage comprised of hydrogen and battery, from the perspective of economic effectiveness. To rapidly evaluate the system...
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This paper carries out a comprehensive analysis on an offshore wind farm equipped with a hybrid storage comprised of hydrogen and battery, from the perspective of economic effectiveness. To rapidly evaluate the system economy, a computationally efficient convex program that takes the nonlinear storage efficiencies into account is provided, which can simultaneously and synergistically optimize the storage sizing and energy management over a long offshore wind cycle. In the analysis, a case study on the optimal configuration and operation of the hybrid storage is thoroughly investigated, answering what the scalings are and how the storage functions in the offshore wind farm. Comparisons to other offshore wind farms with none or only one storage type further demonstrate the advantage of combining hydrogen plant and battery. Influences of the offshore wind electricity price of grid parity and hydrogen price on the system economies, in the terms of total annual cost, net annual profit and hydrogen production cost, are also discussed, revealing sensitivity and dependency of the scalings. Finally, this paper presents the future potential of applying hydrogen plant in the offshore wind farm, from the angles of hydrogen production cost and energy saving. & COPY;2023 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
The Peaceman-Rachford splitting method (PRSM) is an efficient approach for two-block separable convex programming. In this paper we extend this method to the general case where the objective function consists of the s...
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The Peaceman-Rachford splitting method (PRSM) is an efficient approach for two-block separable convex programming. In this paper we extend this method to the general case where the objective function consists of the sum of multiple convex functions without coupled variables, and present a generalized PRSM. Theoretically, we prove global convergence of the new method and establish the worst-case convergence rate measured by the iteration complexity in the ergodic sense for the new method. Numerically, its efficiency is illustrated by synthetic data about the robust principal component analysis (PCA) model with noisy and incomplete information.
In this paper, we devise a new hybrid method for pattern synthesis of large linear arrays. To simplify the beamforming network, the uniform linear array is divided into multiple non-overlapped subarrays with contiguou...
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In this paper, we devise a new hybrid method for pattern synthesis of large linear arrays. To simplify the beamforming network, the uniform linear array is divided into multiple non-overlapped subarrays with contiguous elements and is only weighted at subarrays. Unlike previous approaches, the proposed method introduces a special vector to specify the subarray partition and converts the subarray pattern synthesis to the problem of finding the optimal subarray partition and subarray weighting vectors simultaneously. To solve this problem efficiently, the genetic algorithm is utilized to find the optimal partition scheme from all possible subarray partitions. For the fixed subarray partition, the optimal subarray weighting vector is obtained by solving the convex sub-problem. Numerical results demonstrate the superiority of our method over the state-of-the-art algorithm.
In this paper, we focus on the application of the Peaceman-Rachford splitting method (PRSM) to a convex minimization model with linear constraints and a separable objective function. Compared to the Douglas-Rachford s...
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In this paper, we focus on the application of the Peaceman-Rachford splitting method (PRSM) to a convex minimization model with linear constraints and a separable objective function. Compared to the Douglas-Rachford splitting method (DRSM), another splitting method from which the alternating direction method of multipliers originates, PRSM requires more restrictive assumptions to ensure its convergence, while it is always faster whenever it is convergent. We first illustrate that the reason for this difference is that the iterative sequence generated by DRSM is strictly contractive, while that generated by PRSM is only contractive with respect to the solution set of the model. With only the convexity assumption on the objective function of the model under consideration, the convergence of PRSM is not guaranteed. But for this case, we show that the first t iterations of PRSM still enable us to find an approximate solution with an accuracy of O(1/t). A worst-case O(1/t) convergence rate of PRSM in the ergodic sense is thus established under mild assumptions. After that, we suggest attaching an underdetermined relaxation factor with PRSM to guarantee the strict contraction of its iterative sequence and thus propose a strictly contractive PRSM. A worst-case O(1/t) convergence rate of this strictly contractive PRSM in a nonergodic sense is established. We show the numerical efficiency of the strictly contractive PRSM by some applications in statistical learning and image processing.
A recurrent neural network, called a deterministic annealing neural network, is proposed for solving convex programming problems. The proposed deterministic annealing neural network is shown to be capable of generatin...
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A recurrent neural network, called a deterministic annealing neural network, is proposed for solving convex programming problems. The proposed deterministic annealing neural network is shown to be capable of generating optimal solutions to convex programming problems. The conditions for asymptotic stability, solution feasibility, and solution optimality are derived. The design methodology for determining design parameters is discussed. Three detailed illustrative examples are also presented to demonstrate the functional and operational characteristics of the deterministic annealing neural network in solving linear and quadratic programs.
In this paper, the Iri-Imai algorithm for solving linear and convex quadratic programming is extended to solve some other smooth convex programming problems. The globally linear convergence rate of this extended algor...
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In this paper, the Iri-Imai algorithm for solving linear and convex quadratic programming is extended to solve some other smooth convex programming problems. The globally linear convergence rate of this extended algorithm is proved, under the condition that the objective and constraint functions satisfy a certain type of convexity, called the harmonic convexity in this paper. A characterization of this convexity condition is given. The same convexity condition was used by Mehrotra and Sun to prove the convergence of a path-following algorithm. The Iri-Imai algorithm is a natural generalization of the original Newton algorithm to constrained convex programming. Other known convergent interior-point algorithms for smooth convex programming are mainly based on the path-following approach.
An on-board guidance generation approach for Mars pinpoint landing has been developed based on sequential convex programming. To optimize the flight time in the formulation, a discretized form of the landing problem w...
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An on-board guidance generation approach for Mars pinpoint landing has been developed based on sequential convex programming. To optimize the flight time in the formulation, a discretized form of the landing problem was constructed under the conditions of linearized states, controls, and time increment between consecutive time steps. To implement this strategy in real time, on-board demonstrations were conducted with the GR740, which is the next-generation on-board processor of choice for the European Space Agency. The total number of time steps was determined based on the results of these demonstrations. The numerically simulated results also indicate that the solution obtained via the proposed strategy is close to the optimized GPOPS-II solution under the condition of no disturbance. Even under disturbances such as navigation errors, initial prediction errors, and perturbation forces, the proposed strategy ensures that the spacecraft reaches its target position with near-optimal fuel consumption. (C) 2021 COSPAR. Published by Elsevier B.V. All rights reserved.
We present a new method for minimizing a strictly convex function subject to general convex constraints. Constraints are used one at a time, no changes are made in the constraint functions (thus the row-action nature ...
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We present a new method for minimizing a strictly convex function subject to general convex constraints. Constraints are used one at a time, no changes are made in the constraint functions (thus the row-action nature of the algorithm) and at each iteration a subproblem is solved consisting of minimization of the objective function subject to one or two linear equations. Convergence of the algorithm is established and the method is compared with other row-action algorithms for several relevant particular cases.
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