On Variants of Sliding and Frank-Wolfe Type Methods and Their Applications in Video Co-localization

In this dissertation, our main focus is to design and analyze first-order methods for computing approximate solutions to convex, smooth optimization problems over certain feasible sets. Specifically, our goal in this dissertation is to explore some variants of sliding and Frank-Wolfe (FW) type algorithms, analyze their convergence complexity, and examine their performance in numerical experiments. We achieve three accomplishments in our research results throughout this dissertation. First, we incorporate a linesearch technique to a well-known projection-free sliding algorithm, namely the conditional gradient sliding (CGS) method. Our proposed algorithm, called the conditional gradient sliding with linesearch (CGSls), does not require the knowledge of Lipschitz constant of the gradient of objective function, which is critical in the numerical implementation of the CGS method. Second, we explore the possibility of designing a bundle level type version of the CGS method, which to the best of our knowledge has not yet appeared in the literature. Our proposed sliding APL (SAPL) method achieves the same complexity to the CGS method. Third, we study numerical algorithms for solving the image co-localization problem. For this problem, we propose new variants of the Frank-Wolfe (FW) method and compare their empirical performance with other existing methods. The dissertation is organized as follows. In the first chapter, we review some projection-based and projection-free algorithms, their variants, and their respective advantages and disadvantages. Several useful definitions, theorems, and lemmas are also introduced in this chapter that will be utilized throughout the dissertation. For completeness, we prove most of the known results listed in this chapter (proof deferred to the appendix). In the second chapter, we incorporate a linesearch technique to the well-known CGS method and propose the CGSls method. We show that the proposed CGSls method converges with similar complexity to the CGS method. We also examine the performance of the proposed algorithm by comparing it to the CGS method and other projection-free algorithms. In the third chapter, we explore the possibility of designing a bundle level type variant of the CGS method. The proposed SAPL method is inspired by previous literature on bundle level type method. Such bundle level type method has not yet appeared in any literature on sliding algorithms. We show that the proposed SAPL method converge with the same order of complexity as the CGS and CGSls methods. In the fourth chapter, we apply the algorithms studied in previous chapters to the well-known video co-localization problem. We also propose new variants of the FW method and compare their empirical performance with other numerical methods

A Projection-Free Algorithm for Solving Support Vector Machine Models

In this thesis our goal is to solve the dual problem of the support vector machine (SVM) problem, which is an example of convex smooth optimization problem over a polytope. To this goal, we apply the conditional gradient (CG) method by providing explicit solution to the linear programming (LP) subproblem. We also describe the conditional gradient sliding (CGS) method that can be considered as an improvement of CG in terms of number of gradient evaluations. Even though CGS performs better than CG in terms of optimal complexity bounds, it is not a practical method because it requires the knowledge of the Lipschitz constant and also the number of iterations. As an improvement of CGS, we designed a new method, conditional gradient sliding with line search (CGS-ls) that resolves the issues in CGS method. CGS-ls requires $O(1/\sqrt{1/\epsilon})$ gradient evaluations and $O(1/\epsilon)$ linear optimization calls that achieves the optimal complexity bounds in CGS method. We also compare the performance of our method with CG and CGS methods as numerical results by experimenting them in dual problem of SVM for binary classification of two subsets of the MNIST hand-written digits dataset

Diameter of General Kn\"odel Graphs

The Kn\"odel graph $W_{\Delta,n}$ is a $\Delta$-regular bipartition graph on $n\ge 2^{\Delta}$ vertices and $n$ is an even integer. The vertices of $W_{\Delta,n}$ are the pairs $(i,j)$ with $i=1,2$ and $0\le j\le n/2-1$. For every $j$, $0\le j\le n/2-1$, there is an edge between vertex $(1, j)$ and every vertex $(2,(j+2^k-1) \mod (n/2))$, for $k=0,1,\cdots,\Delta-1$. In this paper we obtain some formulas for evaluating the distance of vertices of the Kn\"odel graph and by them, we provide the formula $diam(W_{\Delta,n})=1+\lceil\frac{n-2}{2^{\Delta}-2}\rceil$ for the diameter of $W_{\Delta,n}$, where $n\ge (2\Delta-5)(2^{\Delta}-2)+4$.Comment: 8 pages, 1 tabl

Measuring relative performance of banking industry using a DEA and TOPSIS

One of the primary concerns in banking industry is to measure the relative importance of banking industry using popular multi criteria decision making (MCDM) techniques such as data envelopment analysis (DEA) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). In this paper, we use these two MCDM techniques to measure the relative efficiencies of 16 private and governmental banks in terms of electronic payment. There are three inputs with DEA methods including the number of issued cards, the number of ATM machines and the number of POSs and there are two outputs including the number of successful ATMs and the number of successful POSs transactions. The proposed study of this paper uses the necessary data of one of Iranian provinces and the results of the implementation of DEA and TOPSIS have indicated that 9 out of 16 banks were efficient. Our study also indicates that mean of relative efficiency for private banks was 82% while this number was 75% for governmental banks

The Principle of Dominance and the Limitation of Changing the Use of Agricultural and Garden Lands

The purpose of the present study was to investigate the principle of dominance and limitations imposed on changing the use of agricultural and garden lands. The former and latter are considered as important subjects continuously debated and discussed. Changing the use of garden and agricultural lands is a theoretically argued subject and is followed by the principal question of: how in the face of the dominance principle, the legal limitations in changing the use of agricultural and garden lands are justifiable? In terms of the method of study.the present research falls into the category of descriptive-analytic researches, and library studies have been conducted to answer the mentioned question. The results of the present study indicate that illegal change of use of agricultural lands is an obvious instance of conflict between personal and societal rights. Because the owner of an agricultural land, due to his/her personal rights is allowed to use the land in any legitimate and legal way he/she desires; however, the rights of the society and the future humans forbids the owner to use the land in ways that would harm the public/society. Based on the stated content, it is concluded that the ownership right is absolutely preserved for the real owner based on the principle of dominance, but in cases where this right is conflictual with societal rights, the societal rights would be counted prioritized over the former, and therefore it would be necessary to control personal rights. This preference has a clear and obvious instance in the context of changing the use of agricultural and garden lands; and it is rational that the society’s right will be dominant over the rights of the owner of agricultural and garden lands

Factors related to pedestrians mortality following road traffic accidents in Tehran and Alborz Provinces, Iran

Background and aims: This study aimed to investigate the deaths and injuries following pedestrian traffic accidents and factors associated with death of pedestrian in Tehran and Alborz provinces. Methods: In this cross-sectional study all traffic accidents related to pedestrians in Tehran and Alborz provinces reported from March 21, 2013 to March 21, 2014 by the traffic police were studied. The Database related to death of Legal Medicine Organization was used in order to determine the exact number of deaths. The standard population of World Health Organization was used in order to calculate the age-standardized incidence rate. We used Chi-square test, T-test and logistic regression to extract statistically significant associations. P-value under 0.05 was considered significant. Result: The age-standardized mortality and injury rate were respectively, 6.1 and 65.1 per 100,000 populations. The pedestrian’s road traffic (PRT) mortality and injury rates in men were 3 and 1.5 times more than women respectively. Statistically significant relationships were observed between the pedestrian’s age, the direct cause in the accident, classification of road, month of occurrence, days of week, type of vehicle, accident location and pedestrian action with the death of pedestrians. Conclusion: Given that the highest incidence rate of death was observed in the age group over 65 years old, it is necessary to pay special attention to the physiologic characteristics of this age group by predicting safety plans and also to provide more secure conditions for this high risk group in accident-prone road sections

Assessing Substances Abuse-Induced Mortality Rates by Autopsy Method in Iran

Background: Substance abuse is among the main causes of preventable diseases and premature deaths worldwide. Despite legal efforts to prevent substance abuse, it has increased and imposed significant economic costs on societies. This analytical cross-sectional study aimed to explore the rate of substance abuse-induced mortality in the provinces of Iran, in 2017. We elaborated an evaluation structure to identify nationwide different substance abuse-related mortality rates. Methods: We employed the retrospective data extracted from autopsy, forensic medicine examination, and demographic characteristics from the recordings in the Iranian Legal Medicine Organization (ILMO). Stata and ArcGIS were applied for data analysis. Results: Nationwide, 3089 substance abuse-related deaths were recorded in the ILMO; the incidence rate was 38.17 per million subjects. The deaths mostly occurred in the 30-39 age group and males accounted for 90% of cases. The provinces of Kermanshah, Lorestan, Fars, Hamadan, and Semnan reported significantly higher rates, compared with the provinces of Mazandaran, West-Azerbaijan, and Golestan with the lowest mortality rates per million (74.72, 69.81, 63.42, 61.70, 58.53 vs. 10.82, 12.11, 14.30, respectively). Mortality rates due to the abuse of methadone (20.29), morphine (12.34), amphetamine (5.32), methamphetamine (7.05), codeine (4.21), tramadol (5.96), benzodiazepine (1.47), and diphenoxylate (0.05) were calculated per million populations of Iran.Conclusion: The obtained data suggested that preventive interventions should focus on the 20-40 age group. Methadone, morphine, and methamphetamine were associated with the highest mortality, compared to other substances; thus, they require effective treatment and preventive programs. Iranian Drug Control Headquarters, police department, and policymakers should act more efficiently regarding a preventive strategic plan in this respect

Temporality in Heidegger’s Early Thought

For the establishment of the fundamental ontology, early Heidegger disregards the vulgar understanding of time and analyzes temporality. He believes that the vulgar understanding of time is the degeneration of the world-time, and the world-time itself is the degeneration of temporality. In Being and Time, Heidegger interprets temporality as the ontological sense of care. Here, this three-part phrase is relied on to interpret temporality in the thought of Heidegger. The ontological counteracts the ontic. The ontic investigation is one that considers the entity present-at-hand and determined. But the ontological investigation focuses on the how-being of an entity that is always anticipating itself by projecting itself upon its possibilities. The sense is not what is revealed at the end of the understanding act; but is what wherein the understandability of something maintains itself, namely, the condition for the possibility of understandability of a thing. Care implies what gives totality and unity to the structural aspects of Dasein. Care, which is the sense of Dasein’s being, is constituted through three items including existence, facticity, and fallenness. Temporality is the ontological sense of care; namely, the condition for the possibility of its understandability. Heidegger analyzes authentic existence to explain this word. The ontological structure of authentic existence is the anticipatory resoluteness towards death. The resolute existence that anticipates to death shows itself in the three ecstasies futurity, having-been, and making-present. Each of these three ecstasies is respectively the sense of one of the items of care. Hence, temporality in its unity is the ontological sense of care