# Faculty Publications - Elijah Polak

## Books

- E. Polak,
*Optimization: Algorithms and Consistent Approximations*, Springer Series in Applied Mathematical Sciences, Vol. 124, New York, NY: Springer-Verlag, 1997. [abstract] - E. Polak,
*Computational Methods in Optimization: A Unified Approach*, R. Bellman, Ed., Mathematics in Science and Engineering, Vol. 77, New York, NY: Academic Press, 1971. [abstract] - M. D. Canon, C. D. Cullum, Jr., and E. Polak,
*Theory of Optimal Control and Mathematical Programming*, McGraw-Hill Series in Systems Science, New York: McGraw-Hill, 1970. [abstract] - E. Wong and E. Polak,
*Notes for a First Course on Linear Systems*, New York: Van Nostrand-Reinhold, 1970. [abstract] - L. A. Zadeh and E. Polak, Eds.,
*System Theory*, Inter-University Electronics Series, Vol. 8, New York: McGraw-Hill, 1969. [abstract] - M. A. Aizerman and F. R. Gantmacher,
*Absolute Stability of Regulator Systems*, E. Polak, Trans., Holden-Day Series in Information Systems, San Francisco, CA: Holden-Day, Inc., 1964. [abstract]

## Selected Articles in journals or magazines

- E. Polak and G. Ribiere, "Note on the convergence of methods of conjugate directions,"
*Revue Francaise d'Informatique et de Recherche Operationnelle*, vol. 3, no. 16, pp. 35-43, Jan. 1969. - N. O. Da Cunha and E. Polak, "Constrained minimization under vector valued-criterial in finite dimensional spaces,"
*J. Mathematical Analysis & Applications*, vol. 19, no. 1, pp. 103-124, July 1967. - M. Canon, C. Cullum, and E. Polak, "Constrained minimization problems in finite-dimensional spaces,"
*SIAM J. on Control*, vol. 4, no. 3, pp. 528-547, Aug. 1966.

## Selected Articles in conference proceedings

- J. S. Maltz, E. Polak, and T. F. Budinger, "Multistart optimisation algorithm for joint spatial and kinetic parameter estimation in dynamic ECT," in
*1998 IEEE Nuclear Science Symp. and Medical Imaging Conf. Conference Record*, Vol. 3, Piscataway, NJ: IEEE Press, 1998, pp. 1567-1573.

## Technical Reports

- H. Chung, E. Polak, and S. S. Sastry, "On the Off-Label Use of Outer Approximations: An External Active Set Strategy," EECS Department, University of California, Berkeley, Tech. Rep. UCB/EECS-2007-127, Oct. 2007. [abstract]
- E. Polak, H. Chung, and S. S. Sastry, "An External Active-Set Strategy for Solving Optimal Control Problems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/EECS-2007-90, July 2007. [abstract]
- E. Polak and M. Wetter, "Generalized pattern search algorithms with adaptive precision function evaluations," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M01/30, 2001.
- E. Polak, "First-Order Algorithms for Optimization Problems with a Maximum Eigenvalue Singular Value Cost and/or Constraints," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M00/17, 2000.
- O. Pironneau and E. Polak, "Consistent Approximations and Approximate Functions and Gradients in Optimal Control," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M00/14, 2000.
- A. Schwartz and E. Polak, "A Family of Projected Descent Methods for Optimization Problems with Simple Bounds," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M95/44, 1995.
- C. Neto and E. Polak, "On the Use of Consistent Approximations for the Optimal Design of Beams," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M94/22, 1994.
- A. Schwartz and E. Polak, "Consistent Approximations for Optimal Control Problems Based on Runge-Kutta Integration," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M94/21, 1994.
- E. Polak, "On the Use of Consistent Approximations in the Solution of Semi-Infinite Optimization and Optimal Control Problems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M92/36, 1992.
- E. Polak and T. Yang, "Moving Horizon Control of Linear Systems with Input Saturation and Plant Uncertainty," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/84, 1991.
- E. Polak and T. Yang, "Moving Horizon Control of Linear Systems with Input Saturation, Disturbances, and Plant Uncertainty," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/83, 1991.
- T. Yang and E. Polak, "Moving Horizon Control of Nonlinear Systems with Input Saturation, Disturbances, and Plant Uncertainty," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/82, 1991.
- E. Polak and T. Yang, "Receding Horizon Control of Linear Systems with Input Saturation, Disturbances, and Plant Uncertainty," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/60, 1991.
- L. He and E. Polak, "Multistart Method with Estimation Scheme for Global Satisfycing Problems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/54, 1990.
- E. Wiest and E. Polak, "A Generalized Quadratic Progamming-Based Phase I-Phase II Method for Inequality- Constrained Optimization," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/46, 1990.
- E. Polak, T. Yang, and D. Mayne, "A Method of Centers Based on Barrier Functions for Solving Optimal Control Problems with Continuum State and Control Constraints," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/31, 1990.
- E. Polak and L. He, "Finite-Termination Schemes for Solving Semi-Infinite Satisfying Problems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/13, 1990. [abstract]
- T. Baker and E. Polak, "On the Optimal Control of System Described by Evolution Equations," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/113, 1989.
- E. Polak and L. He, "Rate Preserving Discretization Strategies for Semi-Infinite Programming and Optimal Control," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/112, 1989.
- E. Wiest and E. Polak, "On the Rate of Convergence of Two Minimax Algorithms," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/111, 1989.
- E. Polak, D. Mayne, and J. Higgins, "On the Extension of Newton's Method to Semi-Infinite Minimax Problems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/92, 1989.
- E. Wiest and E. Polak, "On the Linear Convergence of the Pshenichnyi Method of Linearizations," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/55, 1989.
- E. Polak, "Notes on Fundamentals of Optimization for Engineers," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/40, 1989.
- T. Baker and E. Polak, "An Algorithm for Optimal Slewing of Flexible Structures," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/37, 1989.
- Y. Harn and E. Polak, "Design of a Finite Dimensional Stabilizing Compensator for a Flexible Beam with Point Actuators and Sensors," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/33, 1989.
- E. Polak, "Nonsmooth Optimization Algorithms for the Design of Controlled Flexible Structures," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/10, 1989.
- E. Polak and L. He, "A Unified Phase I-Phase II Method of Feasible Directions for Semi-Infinite Optimization," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/7, 1989.
- P. Harn and E. Polak, "On the Design of Finite Dimensional Stabilizing Compensators for Infinite Dimensional Feedback-Systems Via Semi-Infinite Optimization," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/6, 1989.
- E. Polak, J. Higgins, and D. Mayne, "A Barrier Function Method for Minimax Problems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/64, 1988.
- Y. Harn and E. Polak, "Proportional-Plus-Integral Stabilizing Compensators for a Class of MIMO Feedback Systems with Infinite-Dimensional Plants," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/57, 1988.
- E. Polak and E. Wiest, "A Variable Metric Technique for the Solution of Affinely Parametrized Nondifferentiable Optimal Design Problems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/42, 1988.
- L. He and E. Polak, "An Optimal Diagonalization Strategy for the solution of a Class of Optimal Design Problems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/41, 1988.
- J. Higgins and E. Polak, "Minimizing Pseudo-Convex Functions on Convex Compact Sets," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/22, 1988.
- Y. Harn and E. Polak, "On the Design of Finite Dimensional Stabilizing Compensators for Infinite Dimensional Feedback-Systems Via Semi-Infinite Optimization," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/17, 1988.
- E. Polak, "Minimax Algorithms for Structural Optimization," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/4, 1988.
- S. Daijavad, E. Polak, and R. Tsay, "A Combined Deterministic and Random Optimization Algorithm for the Placement of Macro-Cells," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M87/86, 1987.
- T. Baker and E. Polak, "Computational Experiments in the Optimal Slewing of Flexible Structures," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M87/72, 1987.
- S. Salcudean and E. Polak, "Algorithms for Optimal Design of Feedback Compensators," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M87/60, 1987.
- S. Salcudean and E. Polak, "Algorithms for Optimal Design of Feedback Compensators," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M87/48, 1987.
- E. Polak, D. Mayne, and J. Higgins, "A Superlinearly Convergent Algorithm for Min-Max Problems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M86/103, 1986.
- E. Polak and S. Wuu, "On the Design of Stabilizing Compensators Via Semi-Infinite Optimization," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M86/102, 1986.
- T. Wuu, R. Becker, and E. Polak, "A Diagonalization Technique for the Computation of Sensitivity Functions of Linear Time-Invariant Systems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M86/13, 1986.
- E. Polak and D. Stimler, "On the Efficient Formulation of Worst Case Control System Design," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M85/71, 1985.
- D. Mayne and E. Polak, "An Exact Penalty Function Algorithm for Control Problems with State and Control Constraints," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M85/52, 1985.
- E. Polak and D. Q. Mayne, "Algorithms for Optimization Problems with Exclusion Constraints," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M85/33, 1985.
- E. Polak, "On the Mathematical Foundations of Nondifferentiable Optimization in Engineering Design," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M85/17, 1985.
- E. Polak, S. Salcudean, and D. Mayne, "A Sequential Optimal Redesign Procedure for Linear Feedback Systems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M85/15, 1985.
- E. Polak, D. Mayne, and D. Stimler, "Control System Design via Semi-Infinite Optimization: A Review," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M84/35, 1984.
- E. Polak and D. Mayne, "Theoretical and Software Aspects of Optimization-Based Control System Design," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M84/23, 1984.
- E. Polak, "Notes on the Mathematical Foundations of Nondifferentiable Optimization in Engineering Design," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M84/15, 1984.
- D. Mayne and E. Polak, "Outer Approximation Algorithm for Non- Differentiable Optimization Problems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M83/40, 1983.
- E. Polak, "Optimization-Based Design of SISO Control Systems with Uncertain Plant: Problem Formulation," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M83/16, 1983.
- E. Polak, "A Modified Nyquist Stability Test for Use in Computer-Aided Design," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M83/11, 1983.