Interior Point Method Research Articles

(064) “Condoms and Sexual Health Practices, Knowledge, Attitudes, and Beliefs of Cal Poly San Luis Obispo Students”

Abstract Introduction Sexual wellbeing is a large aspect of college students’ health that continues to be minimally addressed on university campuses. Considering the topic of STIs, it is estimated that people ages 15-24 accounted for almost half of the 26 million new sexually transmitted infections that occurred in the United States in 2018 (CDC, 2018). While there is information on condom and contraceptive usage for college students, there is not much data on the usage and beliefs surrounding condoms and sexual health practices. To further explore the sexual health practices at a university, a mixed-method study was conducted by the Sexual and Reproductive Health Lab during the 2020-21 school year. The study included a survey (n=580) and focus group discussions (n = 16) designed to answer the research questions 1) to what extent are condoms being used by students and 2) what are students’ knowledge, attitudes, and beliefs about condoms and sexual health? Results from the study indicated that while 69% of students engage in sexual activity, sex-based differences are apparent in the desire to use condoms, condoms are only used for vaginal sex, and barrier methods other than external condoms are not being used. Further, conversations prior to sex surrounding STI status and testing are limited. Future interventions are necessary to ensure that current limitations to best safe sex practices are improved through more inclusive sexual education and access to sexual health resources. Objective 1. Describe the factors that students consider when electing whether to use a condom by examining scenarios in which they are used frequently, which partner uses one, and why these scenarios elicit use. 2. Identify what type(s) of sexual acts condoms are currently being used for within the Cal Poly student population in comparison to guidelines for best sexual health practice by asking directly about patterns of use for penetrative vaginal, penetrative anal, and oral sex. 3. Discuss the ways in which health services at the University can better support the specific needs of Cal Poly students by gauging knowledge and certain perceptions on sexual health behaviors and contraceptive use, ultimately using the data to identify areas in which university services can target informative and preventive campaigns and provide access to relevant resources. Methods One-on-one in person or virtual interviews were conducted and asked students about their sexual histories to reveal their experiences using protection, initiating STI status conversations, and circumstances where protection is or is not used. Questions were then asked to evaluate student perceptions of “cleanliness” and clean status conversations. After, the interviews were transcribed via Microsoft Word and NVIVO is being used to code the data. Open coding of the data was first done to create codes and themes of the data and once codes were created, axial coding was done to interpret the data. Results Emerging data from the ongoing study reveals some important trends. Perhaps the most notable emerging finding centralizes on the role of trust in influencing a student’s decision to use a condom, engage in an STI status conversation, and ask for proof of status. Many participants also mentioned trust as a key factor. Another emerging finding reveals that students do not share a universal definition of the word “clean”, but instead the semantic value ranges from the physical environment to personal hygiene habits, to STI status. Furthermore, the use of the word “clean” to describe STI status was nor preferred by the general student population as they believe it propagates the stigma surrounding sex and STIs and implies people are dirty. Conclusions As we have uncovered, students do seem to have some understanding of safe sex practices. In addition, plenty of free barrier methods like condoms and dental dams are available across campus. Therefore, the issues related to lack of conversation and condom use, and subsequent rising rates of transmission, cannot be attributed to lack of knowledge or resources. Other factors, then, appear to be impeding adherence to sexual health best practices. Disclosure Yes, this is sponsored by industry/sponsor: Cal Poly San Luis Obispo. Clarification: Industry funding only - investigator initiated and executed study.

Nonlinear dynamic optimization of marine riser system anti-recoil under a flexible multibody framework

Anti-recoil safety of marine risers is critical for deep water offshore drilling. The challenges of riser anti-recoil optimization stem primarily from two factors: (a) nonlinearities of the violent transient response with various system stages and types of design variables and (b) discontinuities of the objective and constraint functions expressed by max–min over the time domain. In this paper, a nonlinear dynamic optimization model and solution method of marine riser system anti-recoil under a flexible multibody framework is proposed. The objective and constraint functions are elaborately designed to protect the system from dynamic buckling and wellhead and riser collision. Corresponding treatments to system state changes and time step sampling are proposed for numerical sensitivity smoothing. In addition, an extra acceleration constraint is imposed to trim and regularize the feasible domain defined by the discontinuous clearance constraint. Following that, the global convergent method of moving asymptotes (GCMMA) is applied. The presented continuous optimization formulation is numerically tested on a real marine riser platform from the X oil field in the South China Sea with a water depth of 1547 m. The numerical results are compared with those computed using a genetic algorithm (GA), surrogate method and interior point method, and the effectiveness and efficiency of the proposed method is demonstrated.

An Interior Point–Inspired Algorithm for Linear Programs Arising in Discrete Optimal Transport

Discrete optimal transport problems give rise to very large linear programs (LPs) with a particular structure of the constraint matrix. In this paper, we present a hybrid algorithm that mixes an interior point method (IPM) and column generation, specialized for the LP originating from the Kantorovich optimal transport problem. Knowing that optimal solutions of such problems display a high degree of sparsity, we propose a column generation–like technique to force all intermediate iterates to be as sparse as possible. The algorithm is implemented nearly matrix-free. Indeed, most of the computations avoid forming the huge matrices involved and solve the Newton system using only a much smaller Schur complement of the normal equations. We prove theoretical results about the sparsity pattern of the optimal solution, exploiting the graph structure of the underlying problem. We use these results to mix iterative and direct linear solvers efficiently in a way that avoids producing preconditioners or factorizations with excessive fill-in and at the same time guaranteeing a low number of conjugate gradient iterations. We compare the proposed method with two state-of-the-art solvers and show that it can compete with the best network optimization tools in terms of computational time and memory use. We perform experiments with problems reaching more than four billion variables and demonstrate the robustness of the proposed method. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Funding: F. Zanetti received funding from the University of Edinburgh, in the form of a PhD scholarship. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0184 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0184 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Distributed primal-dual method on unbalanced digraphs with row stochasticity

This study investigates distributed convex optimisation that accounts for the inequality constraints over unbalanced directed graphs. In distributed optimisation, agents exchange information on a network to obtain an optimal solution when they only know their own cost function. We propose a distributed primal-dual subgradient method based on a row stochastic weight matrix that is associated with a communication network. In the proposed method, the normalised left eigenvector of the weight matrix is estimated by a consensus algorithm. Then, the subgradient of the Lagrange function is scaled by the estimated values of the left eigenvector to compensate for the imbalance of the information flow in the network. We show that the pair of estimations for the primal and dual problems converge to an optimal primal-dual solution. We also show the relation between the convergence rate of the proposed algorithm and the step-size rule. A numerical example confirms the validity of the proposed method.

Attitudes of women and pharmacists on the opportunity to obtain a progestogen-only pill over the counter – Italian outcomes

Purpose Scrutinizing, among potential providers and users, the perceived claim and interest for over the counter (OTC) accessibility of a progestogen-only pill (POP). Methods Cross-sectional, descriptive study based on an online survey of 1000 women and 100 pharmacists in Italy, part of a larger sample including Germany and Spain. Results Hormonal contraceptive methods are used by 35%; 5% of women reported currently not using contraception, 40% using a barrier method, and 20% a method considered less effective than male condoms (including 16% withdrawal and 4% natural methods and fertility/contraceptive applications). Almost 80% of women felt knowledgeable about the different contraceptive method, but about 1/3 had experienced difficulty accessing their oral contraceptive (OC) in the past two years. Women reacted positively to the proposition of an OTC-POP and 85% agreed that they would discuss the decision to buy it with their doctor; 75% reported they would continue to see their doctor for other reproductive health issues, including screening. The most frequent barrier is cost (reported by 25–33% of women) followed by long waiting times for doctor appointments and lack of personal time to schedule an appointment. Pharmacists (66%) would be likely/fairly likely to recommend the POP after appropriate training, agreeing that the benefits of an OTC-POP included improved access for women, saving them time and giving them more independence. Conclusions Potential users of contraception in Italy have a positive attitude toward OTC-POP, with doctors continuing to have a relevant role. Following training, pharmacists are also positive.

Weighted k-domination problem in fuzzy networks

In real-life scenarios, both the vertex weight and edge weight in a network are hard to define exactly. We can incorporate the fuzziness into a network to handle this type of uncertain situation. Here, we use triangular fuzzy number to describe the vertex weight and edge weight of a fuzzy network G. In this paper, we consider weighted k-domination problem in fuzzy network. The weighted k-domination (WKD) problem is to find a k dominating set D which minimizes the cost f (D) : = ∑u∈Dw (u) + ∑v∈V\D min {∑u∈Sw (uv) |S ⊆ N (v) ∩ D, |S| = k}. First, we put forward an integer linear programming model with a polynomial number of constrains for the WKD problem. If G is a cycle, we design a dynamic algorithm to determine its exact weighted 2-domination number. If G is a tree, we give a label algorithm to determine its exact weighted 2-domination number. Combining a primal-dual method and a greedy method, we put forward an approximation algorithm for general fuzzy network on the WKD problem. Finally, we describe an application of the WKD problem to police camp problem.

Formulation for wave propagation in dissipative media and its application to absorbing layers in elastoplastic analysis using mathematical programming

AbstractIn this article, we propose a new solution scheme for modeling elastoplastic problems with stress wave propagation in dissipative media. The scheme is founded on a generalized Hellinger–Reissner (HR) variational principle. The principle renders the discretized boundary‐value problem into an equivalent second‐order cone programming (SOCP) problem that can be resolved in mathematical programming using the advanced optimization algorithm—the interior point method. In such a way, the developed method not only inherits admirable features of the SOCP‐based finite element method in solving elastoplastic problems but also enables the enforcement of absorbing layers (i.e., Caughey absorbing layer), which is essential in modeling stress wave propagation problems, to absorb wave energy. The proposed scheme is validated via the comparison between analytical and numerical results for seismic wave propagation in dissipative media. Its application to elastoplastic dynamic problems with stress wave propagation is also illustrated to demonstrate its efficiency.

Dynamic Transmission and Computation Resource Optimization for Dense LEO Satellite Assisted Mobile-Edge Computing

A dense satellite-terrestrial integrated mobile-edge computing network (SATIMECN) architecture is developed to meet the computing demands for next generation networks. We formulate an average weighted sum energy consumption minimization problem by jointly considering task ratio allocation of computing or offloading at local and the gateway (GW), ground user terminal (GUT)-satellite association relation, GUT multiple-input and multiple-output (MIMO) precoding, and computation resource allocation at local and the GW. Due to the stochastic property of the optimization problem, we adopt Lyapunov optimization theory to transform it into a deterministic one. Then, we decompose the optimization problem into four subproblems and solve each one iteratively. Specifically, task ratio allocation of computing or offloading at local and the GW is obtained in a closed-form expression using the delay constraint. Then, the binary GUT-satellite association subproblem is solved by the weighted minimum mean-squared error and quadratic transform based fractional programming (QTFP) methods. Moreover, the MIMO precoding subproblem is solved by QTFP and interior point methods. Finally, the computation resource allocation subproblem for local and edge computing is derived in closed-form expressions. Simulation results demonstrate that the tradeoff between the average weighted sum energy consumption and the average queue length can be realized by adjusting the Lyapunov control parameter. Moreover, the proposed MIMO communication and frequency reuse schemes for dense satellite network can realize efficient computation offloading with relative low cost.

An efficient multi parametric kernel function for large and small-update methods interior point algorithm for P*(κ)-horizontal linear complementarity problem

In this paper, we propose the first efficient multi parametric kernel function with logarithmic barrier term. A class of polynomial interior-point algorithms for P*(κ)-horizontal linear complementarity problem based on this kernel function, with parameters pi > 0 for all i ∈ 1, 2, , m, are presented. Then by using some simple analysis tools, we present a primal-dual interior point method (IPM) for P*(κ)-horizontal linear complementarity problems based on this kernel function. At the same time, we derive the complexity bounds small and large-update methods, respectively. In particular, if we take many different values of the parameters, we obtain the best known iteration bounds for the algorithms with large- and small-update methods are derived, namely, O((1 + 2κ)√n(log n)log n/ϵ) and O((1 + 2κ)√n log n/ϵ) respectively. We illustrate the performance of the proposed kernel function by some numerical results that are derived by applying our algorithm.

Global Convergence of Policy Gradient Primal–Dual Methods for Risk-Constrained LQRs

While the techniques in optimal control theory are often model-based, the policy optimization (PO) approach directly optimizes the performance metric of interest. Even though it has been an essential approach for reinforcement learning problems, there is little theoretical understanding of its performance. In this paper, we focus on the risk-constrained linear quadratic regulator (RC-LQR) problem via the PO approach, which requires addressing a challenging non-convex constrained optimization problem. To solve it, we first build on our earlier result that an optimal policy has a time-invariant affine structure to show that the associated Lagrangian function is coercive, locally gradient dominated, and has local Lipschitz continuous gradient, based on which we establish strong duality. Then, we design policy gradient primal-dual methods with global convergence guarantees in both model-based and sample-based settings. Finally, we use samples of system trajectories in simulations to validate our methods.

Linear optimization over homogeneous matrix cones

A convex cone is homogeneous if its automorphism group acts transitively on the interior of the cone. Cones that are homogeneous and self-dual are called symmetric. Conic optimization problems over symmetric cones have been extensively studied, particularly in the literature on interior-point algorithms, and as the foundation of modelling tools for convex optimization. In this paper we consider the less well-studied conic optimization problems over cones that are homogeneous but not necessarily self-dual.We start with cones of positive semidefinite symmetric matrices with a given sparsity pattern. Homogeneous cones in this class are characterized by nested block-arrow sparsity patterns, a subset of the chordal sparsity patterns. Chordal sparsity guarantees that positive define matrices in the cone have zero-fill Cholesky factorizations. The stronger properties that make the cone homogeneous guarantee that the inverse Cholesky factors have the same zero-fill pattern. We describe transitive subsets of the cone automorphism groups, and important properties of the composition of log-det barriers with the automorphisms.Next, we consider extensions to linear slices of the positive semidefinite cone, and review conditions that make such cones homogeneous. An important example is the matrix norm cone, the epigraph of a quadratic-over-linear matrix function. The properties of homogeneous sparse matrix cones are shown to extend to this more general class of homogeneous matrix cones.We then give an overview of the algebraic theory of homogeneous cones due to Vinberg and Rothaus. A fundamental consequence of this theory is that every homogeneous cone admits a spectrahedral (linear matrix inequality) representation.We conclude by discussing the role of homogeneous structure in primal–dual symmetric interior-point methods, contrasting this with the well-developed algorithms for symmetric cones that exploit the strong properties of self-scaled barriers, and with symmetric primal–dual methods for general convex cones.

Contraceptive efficacy and antioxidant potential of Leptadenia reticulata bark extracts in male albino rats

Birth control measures available are primarily for women which are hormonal supplements that are increasing cancer risks and reproductive health issues. Male contraceptive options are effective and available, i.e. barrier methods and vasectomy. Condoms are failure-prone and single-use, while a vasectomy is a permanent sterilization method done surgically, and reversion is not always successful and expensive. A promising oral male contraceptive drug candidate is yet to be discovered. This study investigated the contraceptive efficacy and antioxidant potential of various extracts of Leptadenia reticulata bark in male rats. To study the effects of various extracts (ethanolic and petroleum ether) of L. reticulata bark in male rats, oral administration at the dose level of 250 mg/kg body weight/ day was done for 60 days. Observations were made for body and organ weight, hematology, serum biochemical chemistry, testosterone and antioxidants, lipid profile, sperm parameters (density and motility) and histological changes (reproductive organs). As compared to control in treated groups (TP and bark petroleum ether extract), a significant reduction (P ≤ 0.001) was perceived in sperm motility and density, as well as reproductive organ weight, serum testosterone, and serum antioxidant parameters like SOD. Histological observations revealed arrest in spermatogenesis and reduced seminiferous tubule diameter, mature Leydig cells, secondary spermatogonia, and spermatids which caused a substantial increase in LPO and GSH. From the research findings, it can be concluded that bark petroleum ether extract of L. reticulata possesses contraceptive potential in male albino rats and can serve as a safe and reversible oral contraceptive for males.

A New Stopping Criterion for Krylov Solvers Applied in Interior Point Methods

When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), the attention is usually placed on accelerating their convergence by designing appropriate preconditioners, but the linear solver is applied as a black box with a standard termination criterion which asks for a sufficient reduction of the residual in the linear system. Such an approach often leads to an unnecessary 'oversolving' of linear equations. In this paper, an IPM that relies on an inner termination criterion not based on the residual of the linear system is introduced and analyzed. Moreover, new indicators for the early termination of the inner iterations are derived from a deep understanding of IPM needs. The new technique has been adapted to the Conjugate Gradient (CG) and to the Minimum Residual method (MINRES) applied in the IPM context. The new criterion has been tested on a set of quadratic optimization problems including compressed sensing, image processing and instances with partial differential equation constraints, and it has been compared to standard residual tests with variable tolerance. Evidence gathered from these computational experiments shows that the new technique delivers significant improvements in terms of inner (linear) iterations and those translate into significant savings of the IPM solution time.

APPLICATION OF THE QUASI-NEWTON IN INTERIOR POINT METHODS FOR SOLVING THE PREDISPATCH PROBLEM

Brazilian energy matrix is essentially based on hydroelectricity with long transmission lines, allowing the exchange of energy produced in all regions of the country, the increased demand for energy and the search for lower costs, the application of more efficient and robust methods to minimize generation and transmission losses is necessary, since these are functions of generated and transmitted power, respectively. The purpose of this work is to implement primal dual interior point method for the predispatchof a hydroelectric system, with partial replacement of the Newton method with the quasi-Newton method in order to compute the system Jacobian matrix and reduce the computational costs of the iterations arising from approximations of the inverses of the Hessian matrix. This means that, in order to obtain a search direction, only a matrix vector product is necessary, which is much more efficient, for example, than the Newton method, in which a linear system has to be solved at each iteration. Computational results prove the efficiency of the approach used.

Partially Linear Component Support Vector Machine for Primary Energy Consumption Forecasting of the Electric Power Sector in the United States

Energy forecasting based on univariate time series has long been a challenge in energy engineering and has become one of the most popular tasks in data analytics. In order to take advantage of the characteristics of observed data, a partially linear model is proposed based on principal component analysis and support vector machine methods. The principal linear components of the input with lower dimensions are used as the linear part, while the nonlinear part is expressed by the kernel function. The primal-dual method is used to construct the convex optimization problem for the proposed model, and the sequential minimization optimization algorithm is used to train the model with global convergence. The univariate forecasting scheme is designed to forecast the primary energy consumption of the electric power sector of the United States using real-world data sets ranging from January 1973 to January 2020, and the model is compared with eight commonly used machine learning models as well as the linear auto-regressive model. Comprehensive comparisons with multiple evaluation criteria (including 19 metrics) show that the proposed model outperforms all other models in all scenarios of mid-/long-term forecasting, indicating its high potential in primary energy consumption forecasting.

Awareness and utilization of emergency contraceptives among female nursing students at KIU, western campus, Bushenyi District

Emergency contraception is used as an emergency procedure to prevent unintended pregnancy after an unprotected sexual intercourse and method failure. This study assessed knowledge and utilization of emergency contraception among certificate female nursing students of Kampala International University, western campus. A descriptive cross-sectional study was conducted among female nursing students of Kampala International University in August 2016. Participants were sampled using systematic sampling technique. Pre-tested, self-administered questionnaires were used to collect the data. Data was entered and analyzed using Microsoft excel programme. Results were presented using descriptive statistics, frequencies and percentages. A total of ninety-six (96) volunteered certificate nursing female students participated in the study. Seventy-six (79%) of the female certificate nursing students ever heard of emergency contraceptives (EC), only 8(11%) used/or ever used the method. The commonest source of information was formal health education (71%). EC are indicated in preventing pregnancy post rape (29%), failure of barrier method (24%), missing of oral contraceptives (20%); and should be initiated within 24 hours (43.4%). In addition, students knew that ECs do not terminate pregnancy if the woman is already pregnant (68%), are available not only by prescription (74%), effective when taken immediately (50%) and do not protect and prevent STD (88%). The present study shows that knowledge of emergency contraceptives among certificate female nursing students of Kampala International University is high though utilization of the method is still very low despite some having unintended pregnancies. Evidently, there is a need for carefully designed educational programmes and promotion of EC in student health care centers in the campus. Keywords: Emergency Contraceptives, unintended pregnancy, Bushenyi District, oral contraceptives.

A Primal-Dual Interior-Point Algorithm Based on a Kernel Function with a New Barrier Term

In this paper, we propose a path-following interior-point method (IPM) for solving linear optimization (LO) problems based on a new kernel function (KF). The latter differs from other KFs in having an exponential-hyperbolic barrier term that belongs to the hyperbolic type, recently developed by I. Touil and W. Chikouche \cite{filomat2021,acta2022}. The complexity analysis for large-update primal-dual IPMs based on this KF yields an $\mathcal{O}\left( \sqrt{n}\log^2n\log \frac{n}{\epsilon }\right)$ iteration bound which improves the classical iteration bound. For small-update methods, the proposed algorithm enjoys the favorable iteration bound, namely, $\mathcal{O}\left( \sqrt{n}\log \frac{n}{\epsilon }\right)$. We back up these results with some preliminary numerical tests which show that our algorithm outperformed other algorithms with better theoretical convergence complexity. To our knowledge, this is the first feasible primal-dual interior-point algorithm based on an exponential-hyperbolic KF.

Multi-Objective LQG Design with Primal-Dual Method

The objective of this paper is to investigate a multi-objective linear quadratic Gaussian (LQG) control problem. Specifically, we examine an optimal control problem that minimizes a quadratic cost over a finite time horizon for linear stochastic systems subject to control energy constraints. To tackle this problem, we propose an efficient bisection line search algorithm that outperforms other approaches such as semidefinite programming in terms of computational efficiency. The primary idea behind our algorithm is to use the Lagrangian function and Karush–Kuhn–Tucker (KKT) optimality conditions to address the constrained optimization problem. The bisection line search is employed to search for the Lagrange multiplier. Furthermore, we provide numerical examples to illustrate the efficacy of our proposed methods.

A New Optimal Power Flow Model Considering the Active Power Constraints of Transmission Interfaces

An optimal power flow model as well as algorithm is provided for interconnected power systems considering active power constraints of transmission interfaces. To ensure the optimum operation of an interconnected power system, the optimal goal of the proposed model is minimizing the loss of active power. For satisfying transaction power constraints, the active power constraints of transmission interfaces are taken into account as inequality constraints. Considering the multi-area characteristic of interconnected power systems, a decomposition-coordination optimal model is proposed on the base of the model previously established. And the decomposition-coordination interior point method is used to solve the decomposition-coordination optimal model. Simulations of two test systems illustrate that the proposed model as well as the algorithm can improve computational efficiency, which can provide operation schedule decisions for interconnected power systems.

A stochastic variance-reduced accelerated primal-dual method for finite-sum saddle-point problems

A stochastic variance-reduced accelerated primal-dual method for finite-sum saddle-point problems