Constructing convex inner approximations of steady-state security regions by Nguyen, Hung D., Dvijotham, Krishnamurthy, Turitsyn, Konstantin

“…We propose a scalable optimization framework for estimating convex inner approximations of the steady-state security sets. …”
Get full text

On bounded partition dimension of different families of convex polytopes with pendant edges by Khali, Adnan, Said Husain, Sh. K, Nadeem, Muhammad Faisal

“…Γ is unique then Γ is the resolving partition set of vertices of ψ . The minimum value of j in the resolving partition set is known as partition dimension and written as pd(ψ). …”

A new inexact line search method for convex optimization problems by Moyi, Aliyu Usman, Leong, Wah June

“…Numerical results on a set of standard unconstrained optimization problems showed that the proposed procedure is superior to the Armijo line search.…”
Get full text

Distributed continuous-time nonsmooth convex optimization with coupled inequality constraints by Li, Xiuxian, Xie, Lihuan, Hong, Y.

“…This paper studies distributed convex optimization problems over continuous-time multiagent networks subject to two types of constraints, i.e., local feasible set constraints and coupled inequality constraints, where all involved functions are not necessarily differentiable, only assumed to be convex. …”
Get full text

Regret and cumulative constraint violation analysis for distributed online constrained convex optimization by Yi, Xinlei, Li, Xiuxian, Yang, Tao, Xie, Lihua, Chai, Tianyou, Johansson, Karl Henrik

“…This is a sequential decision making problem with two sequences of arbitrarily varying convex loss and constraint functions. At each round, each agent selects a decision from the decision set, and then only a portion of the loss function and a coordinate block of the constraint function at this round are privately revealed to this agent. …”
Get full text

Distributed bandit online convex optimization with time-varying coupled inequality constraints by Yi, Xinlei, Li, Xiuxian, Yang, Tao, Xie, Lihua, Chai, Tianyou, Johansson, Karl Henrik

“…Distributed bandit online convex optimization with time-varying coupled inequality constraints is considered, motivated by a repeated game between a group of learners and an adversary. …”
Get full text

Some new fractal Milne-type integral inequalities via generalized convexity with applications by Meftah, Badreddine, Lakhdari, Abdelghani, Saleh, Wedad, Kilicman, Adem

“…This study aims to construct some new Milne-type integral inequalities for functions whose modulus of the local fractional derivatives is convex on the fractal set. To that end, we develop a novel generalized integral identity involving first-order generalized derivatives. …”

Protection of line faults in HVDC grids through convexity detection in backward traveling wave voltages by Wang, Ting, Yu, Zexue, Xie, Fan, Hao, Zhiguo, Monti, Antonello, Ponci, Ferdinanda

“…Conventional fault isolation schemes for HVDC grids typically rely on numerical simulations or analytical calculations for threshold setting, which complicate engineering implementation. …”
Get full text

Absolute derivative of set-valued maps by Muslikh, Mohamad, Kilicman, Adem

“…The aim of this article is to develop a differential calculus for setvalued functions with values in metric spaces of the family of all compact and convex subsets. Using only the metric Hausdorff on metric spaces and without using the Hukuhara difference, a concept of the derivative is introduced for set-valued functions in such metric spaces. …”

Extremal properties, coefficient inequalities and radius properties of a certain class of close-to-convex functions / Abdullah Yahya by Yahya, Abdullah

Get full text

The convex polytopes and homogeneous coordinate rings of bivariate polynomials / Shamsatun Nahar Ahmad, Nor’Aini Aris and Azlina Jumadi by Ahmad, Shamsatun Nahar, Aris, Nor’Aini, Jumadi, Azlina

“…Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. …”
Get full text
Get full text

Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation function by Lim, Dong-Young, Neufeld, Ariel, Sabanis, Sotirios, Zhang, Ying

Get full text

Some remarks on local fractional integral inequalities involving Mittag–Leffler kernel using generalized (E, h)-convexity by Saleh, Wedad, Lakhdari, Abdelghani, Almutairi, Ohud, Kilicman, Adem

“…In the present work, we introduce two new local fractional integral operators involving Mittag–Leffler kernel on Yang’s fractal sets. Then, we study the related generalized Hermite– Hadamard-type inequality using generalized (E, h)-convexity and obtain two identities pertaining to these operators, and the respective first- and second-order derivatives are given. …”

Attack-resilient distributed convex optimization of cyber-physical systems against malicious cyber-attacks over random digraphs by Feng, Zhi, Hu, Guoqiang

“…This paper addresses a resilient exponential distributed convex optimization problem for a heterogeneous linear multi-agent system under Denial-of-Service (DoS) attacks over random digraphs. …”
Get full text

ADMM algorithms for matrix completion problem in noisy settings by Le, Tran Kien

“…Meanwhile, Alternating Direction Method of Multiplier is a straightforward but effective algorithm for distributed convex optimization. In this work, we will study ADMM in application to matrix completion problem in the noisy setting. …”
Get full text

A variant of the level set method and applications to image segmentation by Lie, Johan, Lysaker, Marius, Tai, Xue Cheng

“…Further, the reinitializing procedure requested in classical level set methods is superfluous using our approach. The minimization functional for our approach is locally convex and differentiable and thus avoids some of the problems with the nondifferentiability of the Delta and Heaviside functions. …”
Get full text
Get full text
Get full text

Simultaneous spatial and spectral low-rank representation of hyperspectral images for classification by Mei, Shaohui, Hou, Junhui, Chen, Jie, Chau, Lap-Pui, Du, Qian

“…Technically, we formulate S3LRR as a constrained convex optimization problem, and solve it using the efficient inexact augmented Lagrangian multiplier method. …”
Get full text

A Superlinearly Convergent Smoothing Newton Continuation Algorithm for Variational Inequalities over Definable Sets by Chua, Chek Beng, Hien, L. T. K.

“…Optim., 15 (2005), pp. 593--615] to variational inequalities over general closed convex sets X. We prove that when the underlying barrier has a gradient map that is definable in some o-minimal structure, the iterates generated converge superlinearly to a solution of the variational inequality. …”
Get full text
Get full text

Asymptotically locally optimal weight vector design for a tighter correlation lower bound of quasi-complementary sequence sets by Liu, Zilong, Guan, Yong Liang, Mow, Wai Ho

“…A quasi-complementary sequence set (QCSS) refers to a set of two-dimensional matrices with low nontrivial aperiodic auto- and cross-correlation sums. …”
Get full text
Get full text
Get full text

ANALISIS MASALAH EKSTREM FUNGSI PADA RUANG BERNORMA by , QURRATUL AINI, , Dr. Ch. Rini

“…At first, we introduce the convex sets and the convex functions on normed space. …”