62 research outputs found
On updating the inverse of a KKT matrix
No full textA KKT matrix, W say, is symmetric and nonsingular, with a leading nn block that has a conditional positive definite property and a trailing m m block that is identically zero, the dimensions of W being (n+ m)(n+ m). The author requires the inverse matrix H =W explicitly in an iterative algorithm for unconstrained minimization without derivatives, and only one of the first n rows and columns of W is altered on each iteration. The corresponding change to H can be calculated in O(n ) operations. We study the accuracy and stability of some methods for this updating problem, finding that huge errors can occur in the application to optimization, which tend to be corrected on later iterations. Let # be the leading nn submatrix of H. We give particular attention to the remark that the rank of # is only n- m, due to the zero block of W . Thus # can be expressed as the sum of n- m matrices of rank one, and this factorization can also be updated in O(n ) operations. We find, in theory and in practice, that the use of the factored form of # reduces the damage from rounding errors and improves the stability of the updating procedure. These conclusions are illustrated by numerical results from the algorithm for unconstrained minimization
A study on increasing recycling rate of waste desktop computers by subsidy via bi-level programming in Taiwan
No full text碩士本研究利用二階層數學規劃模 (Bi-Level Programming) 模型解析台灣地區廢主機回收費率制訂的問題以提升回收率。逆向回收物流受到整體經濟情勢活絡或蕭條的影響，而回收率隨之波動，並造成環境保護工作缺失。因此我國透過行政院環保署成立回收基金管理委員會 (簡稱基管會) ，對製造商或進口商 (責任業者) 課徵處理費用，並補貼回收處理廠以鼓勵回收作業，期盼降低環境汙染並達資源的有效利用。
就高階目標而言，係以社會福利系統的立場考量： (i) 期望回收率最大，以降低廢棄物污染的機會； (ii) 行政費用比率最小，以促使回收體系有效率的運作；以及 (iii) 補貼費率比最低，以促進回收處理業者有效運用產能。就低階之回收處理業者而言，則期望利潤最大。兩者目標衝突，又相互影響，因此利用兩階段規劃模型決定一個最適的回收處理費率。
此兩階層非線性規劃問題較為複雜，為簡化求解過程以及不增加問題的複雜度，利用KKT最佳化條件 (KKT Optimality Conditions) 轉換以及變數替換，將此模型轉換為一個以高階為主的0-1 非線性規劃問題 (0-1 Non-Linear Programming Problem)。另為進一步了解不同管理意涵，利用Shih et.al (1996) 所提出之模糊趨近法 (Fuzzy Approach) 轉換為一個低階數學規劃模型求解並作比較。分析結果發現，提升台灣廢主機回收率，業者付出的收集成本高低，比調整行政費用比率及補貼費率更具激勵效果。其次，回收率與處理業者補之單位收集成本呈正相關，當處理業者收購價格越高時，回收率越高。另外，當原物料的價格越高時，回收處理業者的收入會越好，如此將有助於提高資源回收處理的意願。最後，KKT轉換法較模糊趨近法需要稍高的補貼費率，但可獲得稍高的回收率。以上分析結果將有利於環保署未來制訂回收政策之參考。This study attempts to decide a recycling subsidy decision so as to improve the recycling rate of waste desktops in Taiwan through a Bi-Level Programming (BLP). The reverse logistic is influenced by recession or depression of macroeconomic which affects the recycling rate and environment protection. Recycling Fund Management Board (RFMB) in Environmental Protection Agency, ROC Government has been established for controlling waste materials by setting up the recycling and treatment fee to recycling industries for increasing recycling rate and decreasing environmental impact.
The upper-level decision unit is based on the viewpoint of social benefits: (i) Expect to have highest recycling rate to reduce the possibility of waste pollution; (ii) Lowest administrative cost ratio to enforce the operation of the whole recycling system; and (iii) Lowest subsidy ratio to improve the productivity of the recycling industries. The lower-level’s is the recycling industries which tries to maximize profits for their recycling operations
The model is a nonlinear BLP and difficult to solve, and we transform the model into a single-level nonlinear programming problem through two method. First, use KKT optimality conditions, and then the transformed problem is a 0-1 non-linear programming problem by variable substitution. Second, through fuzzy approach, the program is transformed into a lower-level nonlinear programming problem. These two approached are compared for a better understanding of managerial control. We found out that the recycling rate is more depending on the acquisition cost than administrative cost and subsidy. The higher recycling ratio comes from higher acquisition cost. The higher revenue of recycling industries comes from higher raw material prices, in which recycling motivation is encouraged. The KKT optimality conditions needs more subsidy than fuzzy approach, but get a higher recycling rate. The results will be beneficial to tariff setting on recycling desktop computers in Taiwan in the future.目錄
第1章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 3
1.3 研究範圍 3
1.4 研究方法與限制 4
1.5 研究內容與架構 4
第2章 文獻回顧 6
2.1 逆物流 6
2.1.1 逆物流的概念及定義 6
2.1.2 從搖籃到搖籃 7
2.2 資源回收 8
2.2.1 資源回收的介紹與定義 8
2.2.2 國內的資源回收 9
2.2.3 廢棄物品回收清除處理補貼費率 12
2.2.4 廢主機回收方式 13
2.2.5 廢主機處理流程 14
2.2.6 影響國內資源回收之關鍵因素 14
2.3 報廢量推估方式 15
2.3.1 使用年限法 15
2.4 羅吉斯迴歸 16
2.5 多階層數學規劃 17
2.5.1 多階層數學規劃定義及特性 17
2.5.2 二階層數學規劃應用 18
2.5.3 二階層數學規劃問題求解方法 19
2.5.4 KKT轉換法 21
2.5.5 模糊數學規劃 22
2.6 小結 24
第3章 廢主機回收費率模型建構 25
3.1 問題描述 25
3.2 基管會現行費率 26
3.2.1 現行資源回收費率公式 26
3.2.2 資源化價值之計算方法 28
3.2.3 原物料價格計價方式 29
3.3 廢主機回收費率模型機制 30
3.3.1 符號說明與假設條件 31
3.3.2 上階目標函數─社會福利系統 33
3.3.3 下階目標函數─資源回收處理業者 34
3.3.4 模型限制式 37
3.4 廢主機回收費率之解算模型 38
3.4.1 參數說明 38
3.4.2 廢主機資源回收問題二階層數學規劃模型 45
3.4.3 建立模糊輔助模型 46
3.5 小結 49
第4章 案例分析 50
4.1 廢主機回收費計算實例 50
4.1.1 KKT最佳化條件轉換 50
4.1.2 KKT最佳化條件轉換求解 51
4.1.3 KKT之0-1非線性規劃模型 52
4.1.4 KKT之0-1非線性規劃模型求解 54
4.1.5 模糊趨近法 54
4.1.6 模糊趨近法求解 57
4.2 結果比較 58
4.3 參數分析 58
4.3.1 KKT0-1求解之參數分析 58
4.3.2 模糊趨近法之參數分析 60
4.3.3 資源化價格的影響 61
4.4 小結 62
第5章 結論與建議 63
5.1 結論 63
5.2 建議 64
參考文獻 65
中文文獻 65
英文文獻 67
附錄A 97年廢主機回收處理成本 69
附錄B 二次迴歸計算過程 70
附錄C二次迴歸式之參數矩陣運算 71
附錄D硬碟之應報廢量與徵收收入推估 72
附錄E電源供應器之應報廢量與徵收收入推估 73
附錄F機殼之應報廢量與徵收收入推估 74
附錄G問卷 75
附錄H問卷資料整理 76
附錄I 羅吉斯迴歸分析 77
附錄J KKT 0-1轉換程式碼 80
附錄K 模糊趨近法程式碼 83
圖目錄
圖 1.1 研究架構流程 5
圖 2.1 逆物流機制 6
圖 2.2 資源回收系統 9
圖 2.3 資源回收管理基金運作方式 11
圖 2.4 廢主機拆解處理流程圖 14
圖 2.5 多階層規劃問題求解方法之分類 20
圖 2.6 目標式隸屬函數圖 23
圖 3.1 廢資訊物品回收處理流程 30
圖 3.2 高低階關係圖 31
圖 3.3 長期成本曲線 35
圖 3.4回收處理總成本 36
圖 4.1 f1的模糊隸屬函數 54
圖 4.2 f2的模糊隸屬函數 54
圖 4.3 f2的模糊隸屬函數 54
圖 4.2 f2的模糊隸屬函數 54
圖 4.3 r''的模糊隸屬函數 55
圖 4.4 Ca的模糊隸屬函數 55
圖 4.5 Cr的模糊隸屬函數 56
圖 4.6 a 的模糊隸屬函數 56
表目錄
表 2.1 環保署公告應回收項目 10
表 2.2應回收廢棄物品回收清除處理補貼費率表 12
表 2.3經濟部對電機電子設備產品之定義 13
表 2.4 使用年限法之分析整理 16
表 3.1統一補貼模式的優劣分析 26
表 3.2環保署公告費率彙整 28
表 3.3 再生料的價格參考來源與訂價方式 29
表 3.4 問卷數據 40
表 3.5 二元羅吉斯迴歸 40
表 3.6 主機報廢機率 41
表 3.7 廢電子電器及資訊物品處理後再生料及廢棄物價格 42
表 3.8 廢主機衍生物組成及處理成效分析表 42
表 3.9 主機板之應報廢量與徵收收入之推估 44
表 3.10範例參數表 48
表 4.1 最佳化條件轉換求解 52
表 4.2 0-1非線性規劃轉換求解 54
表 4.3高低階解算後數值整理 54
表 4.4 模糊趨近法求解 57
表 4.5 三種求解方式之結果 58
表 4.6 KKT 0-1轉換之參數分析-1 59
表 4.7 KKT 0-1轉換之參數分析-2 59
表 4.8 模糊趨近法之參數分析-1 60
表 4.9 模糊趨近法之參數分析-2 60
表 4.10 g1參數分析 61
表 4.11 g2參數分析 62
表 4.12 g8參數分析 62
表 5.1現行費率比較 63
表 5.2 廢主機回收率對應表 63學號: 698620464, 學年度: 9
Comparison of Fuzzy Solution Approaches for a Bilevel Linear Programming Problem
No full text15th International Conference on Application of Fuzzy Systems, Soft Computing and Artificial Intelligence Tools, ICAFS 2022 -- 26 August 2022 through 27 August 2022 -- Budva -- 291409In this study, we consider solution approaches used to solve the proposed bilevel linear programming model for an Industrial Symbiosis network. We first solve this model with the well-known Karush-Kuch-Tucker (KKT) approach. However, transforming a bilevel programming model with the KKT approach increases the number of variables and constraints. For this reason, we use the fuzzy programming approach and the fuzzy goal programming approaches as alternatives to the KKT approach. Next, we compare the results of the KKT approach with these methods and examine the suitability of these approaches to solve our bilevel problem. Unlike previous studies, which claimed that fuzzy approaches mostly outperform the KKT approach, in our case, the best solution is obtained with the KKT approach. This is most probably because these approaches ignore the hierarchical nature of the problem. We believe that more research on fuzzy approaches is needed to evaluate the suitability of these approaches for solving bilevel programming problems. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, TÜBİTAK, (122M223
Repeated tactile stimulation promotes hippocampal neurogenesis and reduces depression-like behaviors
No full text2015-2016 > Other Outputs > Other outputsNot applicableCopyright retained by autho
Single-Loop Multi-Objective Reliability-Based Design Optimization Using Chaos Control Theory and Shifting Vector with Differential Evolution
No full textMulti-objective reliability-based design optimization (MORBDO) is an efficient tool for generating reliable Pareto-optimal (PO) solutions. However, generating such PO solutions requires many function evaluations for reliability analysis, thereby increasing the computational cost. In this paper, a single-loop multi-objective reliability-based design optimization formulation is proposed that approximates reliability analysis using Karush-Kuhn Tucker (KKT) optimality conditions. Further, chaos control theory is used for updating the point that is estimated through KKT conditions for avoiding any convergence issues. In order to generate the reliable point in the feasible region, the proposed formulation also incorporates the shifting vector approach. The proposed MORBDO formulation is solved using differential evolution (DE) that uses a heuristic convergence parameter based on hypervolume indicator for performing different mutation operators. DE incorporating the proposed formulation is tested on two mathematical and one engineering examples. The results demonstrate the generation of a better set of reliable PO solutions using the proposed method over the double-loop variant of multi-objective DE. Moreover, the proposed method requires 6×–377× less functional evaluations than the double-loop-based DE
Alternative KKT conditions for (semi)infinite convex optimization
No full textThis paper is intended to provide an updated survey of recent optimality theory for infinite-dimensional convex programming. It aims at establishing theoretical support for algorithmic developments. Two alternative strategies inspire the approaches presented in the paper. The first one consists of replacing the family of constraints by a single one, appealing to the supremum function, and is based on various characterizations of the subdifferential of the pointwise supremum of convex functions. The second one uses appropriate characterizations of affine consequent inequalities of the constraint system exploiting ad hoc constraint qualifications.The first author was partially supported by ANID grant Fondecyt Regular 1190110 and Centro de Modelamiento Matemático (CMM), ACE210010 and FB210005, BASAL funds for centers of excellence from ANID-Chile. The research of the second and third author is supported by the Research Project PGC2018-097960-B-C21 from MICINN, Spain. The research of the second author is also supported by MICIU of Spain and Universidad de Alicante (Contract Beatriz Galindo BEA- GAL 18/00205), AICO/2021/165 of Generalitat Valenciana, and Basal CMM FB210005. The third author is also supported by the Australian ARC – Discovery Projects DP 180100602
IDENTIFIKASI AHOK DAN PESAN SATIRE DALAM CERPEN “KORUPTOR KITA TERCINTA” KARYA AGUS NOOR (Identification of Ahok’s Character and Satire Message in The Short Story “Our Beloved Corruptors” by Agus Noor)
No full textLahirnya sebuah karya sastra tidak bisa dilepaskan dari konteks sosial, budaya, ataupun politik yang melingkupinya karena sastra merupakan mimesis kehidupan. Dalam menyikapi persoalan korupsi, Agus Noor dalam karya cerpennya menghadirkan dimensi lain, yakni realitas korupsi dan aktor politik yang ada di dalamnya dengan muatan humor satire yang khas. Yang menjadi tujuan dalam penelitian ini ialah mendeskripsikan dan menjelaskan (1) indentifikasi sosok Ahok dalam cerpen KKT karya Agus Noor; (2) pesan satire dalam cerpen KKT karya Agus Noor.Metode yang digunakan dalam penelitian ini ialah deskriptif-kualitatif dengan pendekatan mimesis sastra. Sumber data berupa buku kumpulan cerpen Lelucon Para Koruptor. Data diambil dengan teknik rekam-catat untuk selanjutnya dianalisis dengan model analisis interaktif. Dari hasil kajian, dihasilkan simpulan bahwa (1) Tokoh utama dalam cerpen KKT memiliki identifikasi yang erat dengan sosok Ahok. Identifikasi tersebut didasarkan pada peristiwa yang dialami tokoh dalam cerita dengan realitas Ahok serta melalui karakter keras, lugas, berani, dan bicara ceplas-ceplos apa adanya. (2) Pesan satire dalam cerpen digunakan sebagai media kritik oleh pangarang terhadap realitas korupsi yang dilakukan para koruptor. Pesan satire digunakan oleh pangarang sebagai media alternatif dalam menyampaikan kritik tentang korupsi melalui guyonan “asem” yang segar nan miris.An art work is strongly related to social context, culture, or politic because it reflects the condition of life. For example, in responding corruption problem, Agus Noor in his literary works shows other dimensions such as the reality of corruption and political actors involved inside with the touch of a unique satire humor. The main purpose of this study was to describe and explain (1) the identification of Ahok’s character in the short story “Koruptor Kita Tercinta” (KKT) by Agus Noor; (2) the satire message in short story KKT by Agus Noor. The method used in this study was descriptive-qualitative method with the main data source was taken from the short story collection entitled Jokes of The Corruptors. The data were taken by using “recording-noting” technique to be further analyzed using analysis-interactive model. From the study, there were some conclusions: (1) the main character in the short story jokes of the corruptors has a strong identification with Ahok. That identification was based on the act experienced by the main character in the story which was compared with the reality and also through some characteristics described such as assertive, straightforward, to be brave, and to speak frankly. (2) The satire message contained in the short story was used as the media of critic by the author toward the corruption reality in Indonesia. Satire message was used by the author as an alternative way in conveying critics on corruption in a fresh and ironic way
'The convex-concave algorithm applied to portfolio analysis
No full textMathematical computations are widely used to give some insight into the stock market. We investigate the convex-concave algorithm for nonlinear optimization applied to portfolio analysis, one of its many applications. We will consider the Markowitz mean-variance model with higher order moments added, and look at the preferences for the investor to his odd and even moments. The nonlinear objective functions may not necessarily be convex nor concave. We write the objective function as the sum of a convex and concave function. Using the fact that it is easy to minimize convex functions on convex compact sets (under some assumptions), and linearizing the concave function at a fixed point, we optimize `easy' convex sub-problems at each iteration. This so-called convex-concave procedure is known to converge to a KKT point.Electrical Engineering, Mathematics and Computer ScienceDelft Institute of Applied Mathematic
Details of Second-Order Partial Derivatives of Rigid-Body Inverse Dynamics
No full textThe details of second-order partial derivatives of rigid-body Inverse/Forward
dynamics are provided. Several properties and identities using Spatial Vector
Algebra are listed, along with their detailed derivations. The expressions
build upon previous work by the author on first-order partial derivatives of
inverse dynamics. The first/second-order derivatives are also extended for
systems with external forces. Finally, the KKT Forward dynamics and Impact
dynamics derivatives are derived
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