Dual Bounds for Periodical Stochastic Programs

A construction of the dual of a periodical formulation of infinite-horizon linear stochastic programs with a discount factor is discussed. The dual problem is used for computing a deterministic upper bound for the optimal value of the considered multistage stochastic program. Numerical experiments demonstrate behavior of that upper bound, especially when the discount factor is close to one.

MCMS-STM: An Extension of Support Tensor Machine for Multiclass Multiscale Object Recognition in Remote Sensing Images

The support tensor machine (STM) extended from support vector machine (SVM) can maintain the inherent information of remote sensing image (RSI) represented as tensor and obtain effective recognition results using a few training samples. However, the conventional STM is binary and fails to handle multiclass classification directly. In addition, the existing STMs cannot process objects with different sizes represented as multiscale tensors and have to resize object slices to a fixed size, causing excessive background interferences or loss of object’s scale information. Therefore, the multiclass multiscale support tensor machine (MCMS-STM) is proposed to recognize effectively multiclass objects with different sizes in RSIs. To achieve multiclass classification, by embedding one-versus-rest and one-versus-one mechanisms, multiple hyperplanes described by rank-R tensors are built simultaneously instead of single hyperplane described by rank-1 tensor in STM to separate input with different classes. To handle multiscale objects, multiple slices of different sizes are extracted to cover the object with an unknown class and expressed as multiscale tensors. Then, M-dimensional hyperplanes are established to project the input of multiscale tensors into class space. To ensure an efficient training of MCMS-STM, a decomposition algorithm is presented to break the complex dual problem of MCMS-STM into a series of analytic sub-optimizations. Using publicly available RSIs, the experimental results demonstrate that the MCMS-STM achieves 89.5% and 91.4% accuracy for classifying airplanes and ships with different classes and sizes, which outperforms typical SVM and STM methods.

Global optimality conditions and duality theorems for robust optimal solutions of optimization problems with data uncertainty, using underestimators

<p style='text-indent:20px;'>In this paper, a robust optimization problem, which features a maximum function of continuously differentiable functions as its objective function, is investigated. Some new conditions for a robust KKT point, which is a robust feasible solution that satisfies the robust KKT condition, to be a global robust optimal solution of the uncertain optimization problem, which may have many local robust optimal solutions that are not global, are established. The obtained conditions make use of underestimators, which were first introduced by Jayakumar and Srisatkunarajah [<xref ref-type="bibr" rid="b1">1</xref>,<xref ref-type="bibr" rid="b2">2</xref>] of the Lagrangian associated with the problem at the robust KKT point. Furthermore, we also investigate the Wolfe type robust duality between the smooth uncertain optimization problem and its uncertain dual problem by proving the sufficient conditions for a weak duality and a strong duality between the deterministic robust counterpart of the primal model and the optimistic counterpart of its dual problem. The results on robust duality theorems are established in terms of underestimators. Additionally, to illustrate or support this study, some examples are presented.</p>

A Randomly Weighted Minimum Arborescence with a Random Cost Constraint

We study the minimum spanning arborescence problem on the complete digraph [Formula: see text], where an edge e has a weight We and a cost Ce, each of which is an independent uniform random variable Us, where [Formula: see text] and U is uniform [Formula: see text]. There is also a constraint that the spanning arborescence T must satisfy [Formula: see text]. We establish, for a range of values for [Formula: see text], the asymptotic value of the optimum weight via the consideration of a dual problem.

Diversifikasi dan Optimasi Usahatani Terintegrasi pada Lahan Kering di Desa Musi Kecamatan Gerokgak Kabupaten Buleleng

Tujuan penelitian adalah (1) menganalisis besarnya pendapatan aktual (gross margin) usahatani terintegrasi (2) menganalisis apakah diversifikasi usahatani pada usahatani terintegrasi lahan kering sudah optimal. Metode yang digunakan dalam menentukan sampel pada penilitian ini adalah teknik sensus sample. Teknik sampel ini menggunakan semua anggota SIMANTRI 001 sebagai sampel dengan anggota kelompok sebanyak 20 orang. Analisis pendapatan aktual yang dipergunakan adalah analisis usahatani melalui perhitungan gross margin. Analisis optimasi dan pendapatan maksimun dianalisis menggunakan metode linear programming (LP) yang diselesaikan dengan bantuan software BPLX88. Hasil penelitian menunjukkan bahwa berdasarkan hasil analisis gross margin, dengan rata-rata luas lahan kering sebesar 0,497 ha, diperoleh pendapatan aktual usahatani jagung MT-1, jagung MT-2, kacang tanah dan ternak sapi sebesar Rp. 696.326.650 per tahun. Berdasarkan hasil analisis linear programming yang dilihat dari primal problem solution menunjukkan jagung (PJG1), jagung (PJG2), kacang tanah (PKT) dan sapi (PSAPI) yang diusahakan bersatus basic atau profitable. Hal ini menunjukkan bahwa lahan seluas 0,497 ha telah berkontribusi dalam memperoleh pendapatan maksimum sebesar Rp. 697.333.800 per tahun. Selanjutnya pada dual problem solution, semua kendala lahan per cabang usahatani dengan luas lahan masing-masing tanaman sebesar 9,95 ha telah habis terpakai, Hal ini menunjukkan bahwa kendala lahan jagung MT-1, jagung MT-2, dan kacang tanah berstatus binding atau habis terpakai tanpa ada sisa (slack). Namun sebagian kendala tidak bersifat binding hal ini terlihat pada stok tenaga kerja bulan Januari-Desember yang belum habis digunakan. Berdasarkan analisis optimasi melalui metode linear programming dengan bantuan BLPXX8 terselenggara dengan optimal, hal ini terbukti dengan pendapatan maksimum sebesar Rp. 697.334.000 artinya mengalami peningakatan pendapatan sebesar Rp.1.007.350 (0,14%), dari pendapataan aktual saat penelitiaan sebesar Rp.696.326.650.

Asymptotic Expansions and Strategies in the Online Increasing Subsequence Problem

We study two closely related problems in the online selection of increasing subsequence. In the first problem, introduced by Samuels and Steele (Ann. Probab. 9(6):937–947, 1981), the objective is to maximise the length of a subsequence selected by a nonanticipating strategy from a random sample of given size $n$ n . In the dual problem, recently studied by Arlotto et al. (Random Struct. Algorithms 49:235–252, 2016), the objective is to minimise the expected time needed to choose an increasing subsequence of given length $k$ k from a sequence of infinite length. Developing a method based on the monotonicity of the dynamic programming equation, we derive the two-term asymptotic expansions for the optimal values, with $O(1)$ O ( 1 ) remainder in the first problem and $O(k)$ O ( k ) in the second. Settling a conjecture in Arlotto et al. (Random Struct. Algorithms 52:41–53, 2018), we also design selection strategies to achieve optimality within these bounds, that are, in a sense, best possible.

Mixed E-duality for E-differentiable Vector Optimization Problems Under (Generalized) V-E-invexity

In this paper, a class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. The so-called vector mixed E-dual problem is defined for the considered E-differentiable vector optimization problem with both inequality and equality constraints. Then, several mixed E-duality theorems are established under (generalized) V-E-invexity hypotheses.

Robust duality for generalized convex nonsmooth vector programs with uncertain data in constraints

Robust optimization has come out to be a potent approach to study mathematical problems with data uncertainty. We use robust optimization to study a nonsmooth nonconvex mathematical program over cones with data uncertainty containing generalized convex functions. We study sufficient optimality conditions for the problem. Then we construct its robust dual problem and provide appropriate duality theorems which show the relation between uncertainty problems and their corresponding robust dual problems.

Improvement of Support Vector Machine Algorithm in Big Data Background

With the rapid development of the Internet and the rapid development of big data analysis technology, data mining has played a positive role in promoting industry and academia. Classification is an important problem in data mining. This paper explores the background and theory of support vector machines (SVM) in data mining classification algorithms and analyzes and summarizes the research status of various improved methods of SVM. According to the scale and characteristics of the data, different solution spaces are selected, and the solution of the dual problem is transformed into the classification surface of the original space to improve the algorithm speed. Research Process. Incorporating fuzzy membership into multicore learning, it is found that the time complexity of the original problem is determined by the dimension, and the time complexity of the dual problem is determined by the quantity, and the dimension and quantity constitute the scale of the data, so it can be based on the scale of the data Features Choose different solution spaces. The algorithm speed can be improved by transforming the solution of the dual problem into the classification surface of the original space. Conclusion. By improving the calculation rate of traditional machine learning algorithms, it is concluded that the accuracy of the fitting prediction between the predicted data and the actual value is as high as 98%, which can make the traditional machine learning algorithm meet the requirements of the big data era. It can be widely used in the context of big data.