This talk is an “eye witness account” of the evolution of nonlinear optimization methods over the last 4 decades. Starting from the early days of simplex-inspired methods, to augmented Lagrangians and interior-points, this talk highlights the need for new active set methods and the opportunities (not challenges) provided by stochasticity. We conclude with a few observations about the formulation and solution of optimization problems in supervised learning.
In this talk I will show some very recent results on optimal strategies for betting on individual sequences of binary outcomes, that is betting against a non-stochastic coin. This naturally extends the well-known Kelly strategy to the adversarial domain.
Moreover, I will show some surprising links between betting, online learning, and adaptive stochastic optimization. Solving optimally coin betting will allow to solve optimally all these problems, with the very same algorithm.
Empirically results will be shown as well.
ADMM algorithms have been applied to a variety of problems in the last few years due in part to: the simplicity of the iteration and the ability to exploit problem structure. In this talk, we present an ADMM algorithm for the class of convex quadratic programs (QPs) that arise in the context of Model Predictive Control (MPC) applications. Our convergence analysis allows to establish the convergence rates of the algorithm for feasible and also optimal value for the ADMM parameter (or step-size) that maximizes the rate of convergence. We also present a combination of the ADMM algorithm and Conjugate Gradient method to accelerate convergence. Numerical results on the performance of the algorithm will be presented on benchmark QPs and QPs from Model Predictive Control applications. Time permitting results on infeasible QPs and extensions for 2-stage stochastic QPs will also be presented.
More details can be found at: http://arxiv.org/abs/1411.7288
Over the last several years I have developed a variety of algorithms for faster solution of mixed-integer linear programs, based on a number of insights about branch and bound methods. The seminar will review the insights, the resulting algorithms, and their experimental validation. Topics will include (i) active constraint branching, (ii) branching to force change, (iii) node selection rules based on common patterns seen in MILP solutions, and (iv) general disjunctions.
In this talk, we will present our recent work on two fundamental optimization problems in electric power systems, namely the optimal power flow (OPF) problem and the unit commitment (UC) problem. The first one is highly non-convex, and the second one is subject to significant uncertainty. In the first-part of the talk, we will present three strong second-order cone programming (SOCP) relaxations for solving large-scale AC OPF problems. Extensive computational experiments show that these relaxations have numerous advantages over existing convex relaxations in the literature: their solution quality is extremely close to that of the standard SDP relaxation; their solutions can be directly used to obtain a high quality feasible OPF solution, and they can be solved an order of magnitude faster than the standard SDP relaxation. In the second-part of the talk, we will present our recent work on multistage robust optimization for the UC problem. We propose simplified affine control policies and develop efficient constraint generation algorithms that solve real-world power systems of more than 3000 buses in a time framework suitable for today's industry practice. Extensive computational experiments show that the multistage robust UC model significantly improves economic and reliability performance over existing operational models for power systems with high penetration of renewable energy.
In this talk, we consider two online optimization problems. The first one is the online linear programming problem. In this problem, the underlying optimization problem is a linear program, however, its constraint matrix is revealed column by column along with the corresponding
objective coefficient and a decision variable has to be set each time a column is revealed without observing the future inputs. The goal is to maximize the overall objective function. In this talk, we provide a near-optimal algorithm for this general class of online problems under the assumption of random order of arrival of the columns and some mild conditions on the size of the LP right-handside input. Specifically, our learning-based algorithm works by dynamically updating a threshold price vector at geometric time intervals, where the dual prices learned from the revealed columns in the previous period are used to determine the sequential decisions in the current period. Due to the feature of dynamic learning, the competitiveness of our algorithm improves over the past study of the same problem. We also present a worst-case example showing that the performance of our algorithm is near-optimal.
We then extend the scope of our learning algorithm to solve a generalization of one special case of the online linear program, the online matching problem. In the generalization, the objective function no longer needs to be linear, but could be general concave functions. This formulation has important applications in online adwords allocation problem when there is a convex under-delivery cost, or the click-through rate is concave in the number of impressions. We show that our algorithm is still near-optimal under some conditions on the inputs. Some numerical results are shown to validate the efficiency of our approach.
We consider distributionally robust (DR) single-server scheduling problem variants with a fixed sequence of appointments with random no-shows and service durations. The joint probability distribution is ambiguous and only the support and first moments are given. We study
DR models that incorporate the worst-case expected cost and the worst-case CVaR of waiting, idleness, and overtime as the objective or constraints. To solve the DR models, we derive exact mixed-integer nonlinear reformulations that facilitate decomposition algorithms. We also derive valid inequalities to strengthen the reformulations and accelerate the computation. In particular, in terms of no-show supports, our derivation leads to polynomial-size LP reformulations for the least conservative (i.e., no consecutive no-shows) and most conservative (i.e., arbitrary no-shows) cases. We test various instances, and derive the following insights: (i) accounting for no-shows in DR models significantly shortens waiting, (ii) one can improve the DR model's ability of utilizing distributional information by using reasonably conservative supports, and (iii) the DR models produce schedules having a ``plateau-half-dome'' shape.
In this talk we present an asynchronous multistart algorithm for identifying high-quality local minima. We highlight strong theoretical results that limit the number of local optimization runs under reasonable assumptions. Though the results are valid whether or not the derivative of the objective function exists, the method's efficient use of previously evaluated points makes it well-suited for finding minima when the objective is expensive to evaluate.
All are welcome to attend! Come and ask questions to the best in the field!
Our Advisory Council Members include:
Ray Hoving '69, '71G - Formerly of Bernard Hodes Group
Richard Simek '94, '95G - Hypertherm, Inc.
Karen LaRochelle '99 - LaRochelle Advisors
Ray Pressburger '05 - Accenture
Kathleen Taylor '87 - Johnson & Johnson
Ray Trakimas '76, '77 MBA - IBM
Kurt Lesker IV '05 - Kurt J. Lesker Company
Ray Glemser '83, '84G & '91 Ph.D. - Glemser Technologies
Charles Searight '73 - Vector Growth Partners
Lane Jorgensen '64, '65G - Stonebridge Group
Jennifer Kennedy '02 - Full Circle Systems (Amazon)
Scott Nestler '89 - The University of Notre Dame
Ravi Kulasekaran - '88G - Colabus & Stridus
Sunil Misser '88G - AccountAbility
Jason Lambert '99 - Sikorsky Aircraft of United Tech. Corp.
Please register here: https://www.eventville.com/catalog/eventregistration1.asp?eventid=1011619
Lehigh’s Industrial and Systems Engineering (ISE) Council will be holding their sixth ISE Career Fair on September 16, 2015, a day before the Lehigh University Career Fair on September 17. Employers and students will be able to meet in a personal setting that and discuss the company’s internship/co-op/job opportunities! *This event is for both ISE & HSE (Healthcare Systems Engineering) students. All companies attending will receive a resume book. Registration fees are per company. Sponsor - $130 Sponsors of the Networking event will get a 5 minute presentation during the first half hour of the event. Sponsorship is limited! Regular - $80 Government - $50 Non-Profit - $30 (must send a copy of 501 (c) 3)