@article{gao_fang_gao_luo_medhin_2021, title={A novel kernel-free least squares twin support vector machine for fast and accurate multi-class classification}, volume={226}, ISSN={["1872-7409"]}, DOI={10.1016/j.knosys.2021.107123}, abstractNote={Multi-class classification is an important and challenging research topic with many real-life applications. The problem is much harder than the classical binary classification, especially when the given data set is imbalanced. Hidden nonlinear patterns in the data set can further complicate the task of multi-class classification. In this paper, we propose a kernel-free least squares twin support vector machine for multi-class classification. The proposed model employs a special fourth order polynomial surface, namely the double well potential surface, and adopts the ”one-verses-all” classification strategy. An ℓ2 regularization term is added to accommodate data sets with different levels of nonlinearity. We provide some theoretical analysis of the proposed model. Computational results using artificial data sets and public benchmarks clearly show the superior performance of the proposed model over other well-known multi-class classification methods, in particular for imbalanced data sets.}, journal={Knowledge-Based Systems}, author={Gao, Z. and Fang, S-C and Gao, X. and Luo, J. and Medhin, N.}, year={2021}, month={Aug}, pages={107123} }
 @article{medhin_xu_2021, title={Optimal asset allocation with restrictions on liquidity}, ISSN={["1532-9356"]}, DOI={10.1080/07362994.2021.1959349}, abstractNote={Abstract An optimal asset allocation problem involving restrictions on liquidity is studied in this article. The portfolio consists of liquid and illiquid asset. The portfolio is only allowed to rebalance at particular times. An investor tries to maximize the total utility of a hyperbolic absolute risk aversion function depending on the consumption, which is sourced only from the liquid asset. The optimal policies of the consumption, investment, and allocation are derived. A numerical approximation scheme is developed to show the optimal allocation policy in our model is path-dependent. Paths of the value function and other optimal controls are illustrated to validate our results.}, journal={STOCHASTIC ANALYSIS AND APPLICATIONS}, author={Medhin, Negash and Xu, Chuan}, year={2021}, month={Jul} }
 @article{medhin_xu_2020, title={Nonzero-Sum Stochastic Differential Reinsurance Games with Jump-Diffusion Processes}, volume={187}, ISSN={["1573-2878"]}, DOI={10.1007/s10957-020-01756-0}, number={2}, journal={JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS}, author={Medhin, Negash and Xu, Chuan}, year={2020}, month={Nov}, pages={566–584} }
 @article{medhin_sambandham_2017, title={Impulsive control problem governed by fractional differential equations and applications}, volume={26}, number={1}, journal={Dynamic Systems and Applications}, author={Medhin, N. G. and Sambandham, M.}, year={2017}, pages={37–63} }
 @book{berkovitz_medhin_2013, title={Nonlinear optimal control theory}, DOI={10.1201/b12739}, abstractNote={Examples of Control Problems Introduction A Problem of Production Planning Chemical Engineering Flight Mechanics Electrical Engineering The Brachistochrone Problem An Optimal Harvesting Problem Vibration of a Nonlinear Beam Formulation of Control Problems Introduction Formulation of Problems Governed by Ordinary Differential Equations Mathematical Formulation Equivalent Formulations Isoperimetric Problems and Parameter Optimization Relationship with the Calculus of Variations Hereditary Problems Relaxed Controls Introduction The Relaxed Problem Compact Constraints Weak Compactness of Relaxed Controls Filippov's Lemma The Relaxed Problem Non-Compact Constraints The Chattering Lemma Approximation to Relaxed Controls Existence Theorems Compact Constraints Introduction Non-Existence and Non-Uniqueness of Optimal Controls Existence of Relaxed Optimal Controls Existence of Ordinary Optimal Controls Classes of Ordinary Problems Having Solutions Inertial Controllers Systems Linear in the State Variable Existence Theorems Non Compact Constraints Introduction Properties of Set Valued Maps Facts from Analysis Existence via the Cesari Property Existence without the Cesari Property Compact Constraints Revisited The Maximum Principle and Some of its Applications Introduction A Dynamic Programming Derivation of the Maximum Principle Statement of Maximum Principle An Example Relationship with the Calculus of Variations Systems Linear in the State Variable Linear Systems The Linear Time Optimal Problem Linear Plant-Quadratic Criterion Problem Proof of the Maximum Principle Introduction Penalty Proof of Necessary Conditions in Finite Dimensions The Norm of a Relaxed Control Compact Constraints Necessary Conditions for an Unconstrained Problem The epsilon-Problem The epsilon-Maximum Principle The Maximum Principle Compact Constraints Proof of Theorem 6.3.9 Proof of Theorem 6.3.12 Proof of Theorem 6.3.17 and Corollary 6.3.19 Proof of Theorem 6.3.22 Examples Introduction The Rocket Car A Non-Linear Quadratic Example A Linear Problem with Non-Convex Constraints A Relaxed Problem The Brachistochrone Problem Flight Mechanics An Optimal Harvesting Problem Rotating Antenna Example Systems Governed by Integrodifferential Systems Introduction Problem Statement Systems Linear in the State Variable Linear Systems/The Bang-Bang Principle Systems Governed by Integrodifferential Systems Linear Plant Quadratic Cost Criterion A Minimum Principle Hereditary Systems Introduction Problem Statement and Assumptions Minimum Principle Some Linear Systems Linear Plant-Quadratic Cost Infinite Dimensional Setting Bounded State Problems Introduction Statement of the Problem epsilon-Optimality Conditions Limiting Operations The Bounded State Problem for Integrodifferential Systems The Bounded State Problem for Ordinary Differential Systems Further Discussion of the Bounded State Problem Sufficiency Conditions Nonlinear Beam Problem Hamilton-Jacobi Theory Introduction Problem Formulation and Assumptions Continuity of the Value Function The Lower Dini Derivate Necessary Condition The Value as Viscosity Solution Uniqueness The Value Function as Verification Function Optimal Synthesis The Maximum Principle Bibliography Index}, publisher={Boca Raton: CRC Press}, author={Berkovitz, L. D. and Medhin, N. G.}, year={2013} }
 @article{medhin_wan_2009, title={Multi-new product competition in duopoly: A differential game analysis}, volume={18}, number={2}, journal={Dynamic Systems and Applications}, author={Medhin, N. G. and Wan, W.}, year={2009}, pages={161–178} }
 @article{banks_hood_medhin_2008, title={A molecular based model for polymer viscoelasticity: Intra- and inter-molecular variability}, volume={32}, ISSN={["1872-8480"]}, DOI={10.1016/j.apm.2007.09.018}, abstractNote={We develop dynamic equations for rubber viscoelasticity based on a stick-slip continuum molecular-based model. The model developed is a continuum tube reptation model in which a chemically cross-linked (CC) system of molecules act as constraint box per unit volume for a physically constrained (PC) system of molecules. The CC-system carries along the PC-system during instantaneous step deformations. The subsequent relaxation of the PC-system is determined by the configuration of the CC-system, its own configuration and confirmation, and external force fields. Conversely, the deformation of the PC-system acts as an internal variable affecting the deformations of the constraining CC-system. We model the relationship between these processes to derive a model of viscoelasticity in rubber deformation. In developing a relaxation process for the PC-system, we start from the fact that the PC-system is composed of long molecular chains. The dynamics of these molecular chains are developed by modelling them as chains of beads connected by springs, which represent inter-molecular potentials. Various segments of the molecular chains relax at different rates. In addition, variability in relaxation times across molecular chains is permitted.}, number={12}, journal={APPLIED MATHEMATICAL MODELLING}, author={Banks, H. T. and Hood, J. B. and Medhin, N. G.}, year={2008}, month={Dec}, pages={2753–2767} }
 @article{banks_hood_medhin_samuels_2008, title={A stick-slip/Rouse hybrid model for viscoelasticity in polymers}, volume={9}, ISSN={["1468-1218"]}, DOI={10.1016/j.nonrwa.2007.06.015}, abstractNote={A Rouse model for polymer chains is incorporated into the linear continuous stick-slip molecular-based tube reptation ideas of Doi–Edwards and Johnson–Stacer. This treats the physically constrained (PC) molecular stretches as internal strain variables for the overall PC/chemically cross-linked (CC) system. It yields an explicit system of stress–strain equations for the system permitting simple calculations of complex stress–strain relations. The model that is developed here treats PC molecule as entrapped within a constraining tube, which is comprised of both CC and PC molecules. The model is compared with experimental data sets from the literature.}, number={5}, journal={NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS}, author={Banks, H. T. and Hood, J. B. and Medhin, N. G. and Samuels, J. S., Jr.}, year={2008}, month={Dec}, pages={2128–2149} }
 @article{banks_medhin_pinter_2008, title={Modeling of viscoelastic shear: A nonlinear stick-slip formulation}, volume={17}, number={2}, journal={Dynamic Systems and Applications}, author={Banks, H. T. and Medhin, N. G. and Pinter, G. A.}, year={2008}, pages={383–405} }
 @article{banks_medhin_pinter_2007, title={Multiscale Considerations in Modeling of Nonlinear Elastomers}, volume={8}, ISSN={1550-2287 1550-2295}, url={http://dx.doi.org/10.1080/15502280601149346}, DOI={10.1080/15502280601149346}, abstractNote={We present a survey of results from an extended project focused on the understanding of the dynamic behavior of elastomers or filled rubbers. This entailed experimental, modeling, computational and theoretical efforts. Of particular emphasis are the nonlinear and hysteretic aspects of dynamic deformations.}, number={2}, journal={International Journal for Computational Methods in Engineering Science and Mechanics}, publisher={Informa UK Limited}, author={Banks, H. T. and Medhin, Negash G. and Pinter, Gabriella A.}, year={2007}, month={Feb}, pages={53–62} }
 @article{medhin_sambandham_2005, title={On minimizing sequences for an optimization problem governed by an integral equation}, volume={14}, number={04-Mar}, journal={Dynamic Systems and Applications}, author={Medhin, N. G. and Sambandham, M.}, year={2005}, pages={607–614} }
 @article{banks_medhin_pinter_2004, title={Nonlinear reptation in molecular based hysteresis models for polymers}, volume={62}, ISSN={["1552-4485"]}, DOI={10.1090/qam/2104273}, abstractNote={We extend the linear “stick-slip” models of Doi-Edwards and Johnson-Stacer to nonlinear tube reptation models. We then show that such models, when combined with probabilistic formulations allowing distributions of relaxation times, provide a good description of dynamic experiments with highly filled rubber in tensile deformations. A connection to other applications including dielectric polarization and reptation in other viscoelastic materials (e.g., living tissue) is noted.}, number={4}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Banks, HT and Medhin, NG and Pinter, GA}, year={2004}, month={Dec}, pages={767–779} }
 @article{ladde_medhin_sambandham_2003, title={Error estimates for random boundary value problems with applications to a hanging cable problem}, volume={38}, DOI={10.1016/S0895-7177(03)00315-7}, number={10}, journal={Mathematical and Computer Modelling}, author={Ladde, G. S. and Medhin, N. G. and Sambandham, M.}, year={2003}, pages={1037–1050} }
 @article{banks_begashaw_medhin_2002, title={Analytical and numerical treatment of a curved active constrained layer structure}, volume={11}, number={1}, journal={Dynamic Systems and Applications}, author={Banks, H. T. and Begashaw, N. and Medhin, N. G.}, year={2002}, pages={75–87} }