In the first part of the tutorial, we introduced the problem of unconstrained optimization, provided necessary and sufficient conditions for optimality of a solution to this problem, and described the gradient descent method for finding a (locally) optimal solution to a given unconstrained optimization problem. We now describe another method for unconstrained optimization, namely Newton’s metho...

Convex optimization solvers are widely used in the embedded systems that require sophisticated algorithms including model predictive control (MPC). In this paper, we aim to reduce online solve time of such convex so as total runtime algorithm and make it suitable for real-time optimization. We exploit property Karush–Kuhn–Tucker (KKT) matrix involved solution problem only some parts change duri...

We address the problem of self-supervised learning for predicting shape supporting terrain (i.e. which will provide rigid support robot during its traversal) from sparse input measurements. The method exploits two types ground-truth labels: dense 2.5D maps and poses, both estimated by a usual SLAM procedure offline recorded show that poses are required because straightforward supervised 3D only...

In this article, we discuss an exact algorithm for solving mixed integer concave minimization problems. A piecewise inner-approximation of the function is achieved using auxiliary linear program that leads to a bilevel program, which provides lower bound original problem. The reduced single level formulation with help Karush–Kuhn–Tucker (KKT) conditions. Incorporating KKT conditions lead comple...

In this paper, we study a class of optimization problems, called Mathematical Programs with Cardinality Constraints (MPCaC). This kind problem is generally difficult to deal with, because it involves constraint that not continuous neither convex, but provides sparse solutions. Thereby reformulate MPCaC in suitable way, by modeling as mixed-integer and then addressing its counterpart, which will...

به دنبال شیوع ویروس کرونا در جهان، بسیاری از تعاملات رسمی آموزشی سمت برگزاری بستر محیط مجازی سوق یافت و ادامة فرایند آموزش معماری نیز همانند همة دوره‌های آموزشی، دلیل تعطیلی دانشگاه‌ها، تنها برخط ممکن گشت. این میان کارگاه‌های طراحی معماری، منزلة کانون ویژگی‌های منحصربه‌فردی دارند که را سایر رشته‌های دانشگاهی جدا کرده است. نمونة بارزی یک مشارکتی، چندحسی، تجربه‌گرای مبتنی بر مسئله همین ویژگی‌ها م...

Non-orthogonal multiple access (NOMA) is a technology that can provide efficient spectrum utilization and increased channel capacity on Internet of Things (IoT) networks. One factor affecting NOMA system performance in the IoT network allocation power for each user. To improve system, this paper presents method optimizing an with Lagrange multiplier using Karush-Kuhn-Tucker (KKT) condition. The...