Pavlo Krokhmal

Interests

Teaching

Probability and statistics, stochastic processes, decision making under uncertainty, optimization

Research

Stochastic optimization, Decision making under uncertainty, Risk analysis, Probabilistic and stochastic combinatorial optimization, Financial engineering, Optimal trading strategies, Pricing of derivatives,Multidisciplinary optimization, Cooperative control and decision making,Computational and applied mathematics, Continuum mechanics

Courses

Scholarly Contributions

Chapters

• Dashti, H., & Krokhmal, P. (2017). A model for optimal reinforcement of error- and attack-resilient clusters in networks under uncertainty. In Optimization Methods and Applications(pp 97-119). Springer.
• Rysz, M., Pajouh, F., Krokhmal, P., & Pasiliao, E. L. (2014). On risk-averse weighted k-club problems. In Examining Robustness and Vulnerability of Critical Infrastructure Networks(pp 231--242).
• Rysz, M., Krokhmal, P., & Pasiliao, E. (2013). Minimum risk maximum clique problem. In Dynamics of Information Systems: Algorithmic Approaches(pp 251--267). Springer.
• Mirghorbani, M., Krokhmal, P., & Pasiliao, E. (2012). Computational Studies of Randomized Multidimensional Assignment Problems. In Dynamics of Information Systems: Mathematical Foundations(pp 225--244). Springer.
• Kammerdiner, A., Krokhmal, P., & Pardalos, P. (2007). On Some Characteristics of the Distribution of Hamming Distance Values Between Solutions of Multidimensional Assignment Problem. In Advances in Cooperative Control and Optimization(pp 293--310). Springer.
• Krokhmal, P., & Jeffcoat, D. (2007). Distributed Cooperative Systems with Human Operator-in-the-Loop. In Advances in Cooperative Control and Optimization(pp 293-310). Springer.
• Jeffcoat, D., Krokhmal, P., & Zhupanska, O. (2006). A Markov Chain Approach to Analysis of Cooperation in Search Missions. In Cooperative Systems: Control and Optimization(pp 171--184). Springer.
• Krokhmal, P., & Murphey, R. (2006). Modeling and Implementation of Risk-Averse Preferences in Stochastic Programs Using Risk Measures. In Robust Optimization-Directed Design(pp 95--116). Springer.
• Krokhmal, P., Uryasev, S., & Zrazhevsky, G. (2005). Numerical Comparison of CVaR and CDaR Approaches: Application to Hedge Funds. In Applications of Stochastic Programming(pp 609--631). SIAM.
• Krokhmal, P., Murphey, R., Pardalos, P., Uryasev, S., & Zrazhevsky, G. (2003). Robust Decision Making: Addressing Uncertainties in Distributions. In Cooperative Control: Models, Applications and Algorithms(pp 165--185). Kluwer Academic Publishers.
• Krokhmal, P. (1995). Motion of a Rigid Annular Plate in a Stokes Fluid. In Contemporary Research in Physics and Mathematics of Young Scientists of Ukraine(pp 72--79).

Journals/Publications

• Borrero, J. S., Prokopyev, O., & Krokhmal, P. (2019). Optimization of Cascading Processes in Arbitrary Networks with Stochastic Interactions. IEEE Transactions on Network Science and Engineering, 6(4), 773--787.
• Chernikov, D., Zhupanska, O., & Krokhmal, P. (2018). Optimization of Dynamic Mechanical Response of a Composite Plate Using Multi-Field Coupling with Thermal Constraints. Applied Mathematical Modeling, 58, 19-32. doi:10.1016/j.apm.2018.01.041
• Rysz, M., Pajouh, F., Krokhmal, P., & Pasiliao, E. L. (2018). Identifying risk-averse low-diameter clusters in graphs with stochastic vertex weights. Annals of Operations Research, 262(1), 89-108. doi:10.1007/s10479-016-2212-6
• Sun, B., Krokhmal, P., & Chen, Y. (2018). Risk-Averse Capacity Planning for Renewable Energy Production. Energy Systems, 9(2), 223-256.
• Rysz, M., Krokhmal, P., & Pasiliao, E. L. (2017). Detecting resilient structures in stochastic networks: A two-stage stochastic optimization approach. Networks, 69(2), 189-204. doi:DOI:10.1002/net.21727
• Vinel, A., & Krokhmal, P. (2017). Certainty equivalent measures of risk. Annals of Operations Research, 249(1), 75--95.
• Vinel, A., & Krokhmal, P. (2017). Mixed-Integer Programming with a Class of Nonlinear Convex Constraints. Discrete Optimization, 24, 66-86. doi:10.1016/j.disopt.2016.07.002
• Chernikov, D., Krokhmal, P., Zhupanska, O. I., & Pasiliao, C. L. (2015). A two-stage stochastic PDE-constrained optimization approach to vibration control of an electrically conductive composite plate subjected to mechanical and electromagnetic loads. Structural and Multidisciplinary Optimization, 52, 227--352.
• Rysz, M., Vinel, A., Krokhmal, P., & Pasiliao, E. L. (2015). A scenario decomposition algorithm for stochastic programming problems with a class of downside risk measures. INFORMS Journal on Computing, 27, 416--430.
• Krokhmal, P., & Prokopyev, O. (2014). Optimization Letters Best Paper Award. Optimization Letters, 8, 2153--2154.
• Rysz, M., Mirghorbani, M., Krokhmal, P., & Pasiliao, E. L. (2014). On risk-averse maximum weighted subgraph problems. Journal of Combinatorial Optimization, 28, 167-185.
• Vinel, A., & Krokhmal, P. (2014). On valid inequalities for mixed integer $p$-order cone programming. Journal of Optimization Theory and Applications, 160, 439--456.
• Vinel, A., & Krokhmal, P. (2014). Polyhedral approximations in $p$-order cone programming. Optimization Methods \& Software, 29, 1210--1237.
• Krokhmal, P., & Prokopyev, O. (2013). Editorial. Optimization Letters, 7, 1--2.
• Mirghorbani, M., & Krokhmal, P. (2013). On finding k-cliques in k-partite graphs. Optimization Letters, 7, 1155--1165.
• Morenko, Y., Vinel, A., Yu, Z., & Krokhmal, P. (2013). On $p$-cone linear discrimination. European Journal of Operational Research, 231, 784--789.
• Cannon, J., Krokhmal, P., Chen, Y., & Murphey, R. (2012). Detection of temporal changes in operator functional state using statistical process control methods. Computer Methods and Programs in Biomedicine, 107, 367--381.
• Veremyev, A., Boginski, V., Krokhmal, P., & Jeffcoat, D. (2012). Dense Percolation in Large-Scale Mean-Field Random Networks Is Provably ``Explosive". PLOS ONE, 7, e51883.
• Krokhmal, P., Zabarankin, M., & Uryasev, S. (2011). Modeling and optimization of risk. Surveys in Operations Research and Management Science, 16, 49--66.
• Cannon, J., Krokhmal, P., Lenth, V., & Murphey, R. (2010). An algorithm for online detection of temporal changes in operator cognitive state using real-time psychophysiological data. Biomedical Signal Processing and Control, 5, 229--236.
• Kammerdiner, A., Krokhmal, P., & Pardalos, P. M. (2010). On the Hamming distance in combinatorial optimization problems on hypergraph matchings. Optimization Letters, 4, 609--617.
• Krokhmal, P. A., & Soberanis, P. (2010). Risk optimization with $p$-order conic constraints: A linear programming approach. European Journal of Operational Research, 201, 653--671.
• Krokhmal, P., & Jeffcoat, D. (2010). On measures of cooperation in distributed systems under uncertainties. Military Operations Research, 15, 39--53.
• Krokhmal, P., & Pardalos, P. M. (2009). Random Assignment Problems. European Journal of Operational Research, 194, 1--17.
• Grundel, D., Krokhmal, P., Oliveira, C., & Pardalos, P. M. (2007). On the Number of Local Minima for the Multidimensional Assignment Problem. Journal of Combinatorial Optimization, 13, 1--18.
• Krokhmal, P. (2007). Higher moment coherent risk measures. Quantitative Finance, 7, 373--387.
• Krokhmal, P., & Uryasev, S. (2007). A Sample-Path Approach to Optimal Position Liquidation. Annals of Operations Research, 152, 193-225.
• Krokhmal, P., Grundel, D., & Pardalos, P. (2007). Asymptotic Behavior of the Expected Optimal Value of the Multidimensional Assignment Problem. Mathematical Programming, 109, 525--551.
• Zabarankin, M., & Krokhmal, P. (2007). Generalized Analytic Functions in 3D Stokes Flows. The Quarterly Journal of Mechanics and Applied Mathematics, 60, 99--123.
• Jeffcoat, D., Krokhmal, P., & Zhupanska, O. (2006). Effects of Cueing in Cooperative Search. Naval Research Logistics, 53, 814--821.
• Krokhmal, P., Rockafellar, R. T., & Uryasev, S. (2006). Risk management and optimization in finance. Journal of Banking & Finance, 30, 2--3.
• Grundel, D., Krokhmal, P., Oliveira, C., & Pardalos, P. M. (2005). On the average case behavior of the multidimensional assignment problem. Pacific Journal of Optimization, 1, 39--57.
• Krokhmal, P. (2002). Exact Solution of the Displacement Boundary-Value Problem of Elasticity for a Torus. Journal of Engineering Mathematics, 44, 345--368.
• Krokhmal, P., Palmquist, J., & Uryasev, S. (2002). Portfolio optimization with conditional value-at-risk objective and constraints. Journal of Risk, 4, 43--68.
• Krokhmal, P., Uryasev, S., & Zrazhevsky, G. (2002). Risk Management for Hedge Fund Portfolios: A Comparative Analysis of Linear Rebalancing Strategies. Journal of Alternative Investments, 5, 10-29.
• Krokhmal, P. A. (1999). Axisymmetric displacement boundary-value problem of elasticity for a torus. Bulletin of Kiev University, Series of Physical-Mathematical Sciences, 30--35.
• Krokhmal, P. A. (1999). Exact Solution of the Second Fundamental Boundary-Value Problem of Elasticity for a Torus. Reports of the National Academy of Sciences of Ukraine, 68--72.
• Krokhmal, P. A. (1999). Two Elasticity Problems for a Space with a Rigid Toroidal Inclusion. Mashinoznavstvo, 32--38.
• Krokhmal, P. A., & Ulitko, A. F. (1998). Exact Solution of the Stokes Equations for a Torus. Bulletin of Kiev University, Series of Mathematics and Mechanics, 48--55.