Repository – Page 210 – Optimization Online

Dynamic string-averaging CQ-methods for the split feasibility problem with percentage violation constraints arising in radiation therapy treatment planning

Published: 2021/01/04

Biomedical Applications, Nonlinear Optimization common fixed points, cq-algorithm, cutter operator, dose-volume constraints, percentage violation constraints, radiation therapy treatment planning, split feasibility, string-averaging

We study a feasibility-seeking problem with percentage violation constraints. These are additional constraints, that are appended to an existing family of constraints, which single out certain subsets of the existing constraints and declare that up to a specified fraction of the number of constraints in each subset is allowed to be violated by up to … Read more

Distributionally robust second-order stochastic dominance constrained optimization with Wasserstein distance

Published: 2021/01/03, Updated: 2021/10/19

We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the empirical distribution. We adopt the sample approximation approach to develop a linear programming formulation that provides a lower bound. We propose a novel split-and-dual decomposition … Read more

Model-Free Assortment Pricing with Transaction Data

Published: 2021/01/03, Updated: 2021/01/05

Applications - OR and Management Sciences, Approximation Algorithms, Robust Optimization

We study a problem in which a firm sets prices for products based on the transaction data, i.e., which product past customers chose from an assortment and what were the historical prices that they observed. Our approach does not impose a model on the distribution of the customers’ valuations and only assumes, instead, that purchase … Read more

The structure of conservative gradient fields

Published: 2021/01/03

Adrian Lewis

Tonghua Tian

Nonsmooth Optimization automatic differentiation, clarke subdifferential, conservative field, deep learning, semi-algebraic, stratification, subgradient descent, variational analysis

The classical Clarke subdifferential alone is inadequate for understanding automatic differentiation in nonsmooth contexts. Instead, we can sometimes rely on enlarged generalized gradients called “conservative fields”, defined through the natural path-wise chain rule: one application is the convergence analysis of gradient-based deep learning algorithms. In the semi-algebraic case, we show that all conservative fields are … Read more

An (s^r)hBcResolution ODE Framework for Understanding Discrete-Time Algorithms and Applications to the Linear Convergence of Minimax Problems

Published: 2021/01/02

Haihao Lu

Convex and Nonsmooth Optimization, Convex Optimization, Nonlinear Optimization minimax problems, ode, optimization

There has been a long history of using ordinary differential equations (ODEs) to understand the dynamic of discrete-time algorithms (DTAs). Surprisingly, there are still two fundamental and unanswered questions: (i) it is unclear how to obtain a \emph{suitable} ODE from a given DTA, and (ii) it is unclear the connection between the convergence of a … Read more

Optimization with learning-informed differential equation constraints and its applications

Published: 2021/01/01

Guozhi Dong

Michael Hintermueller

Kostas Papafitsoros

Biomedical Applications, Infinite Dimensional Optimization, Nonlinear Optimization

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through data-driven techniques are studied. A particular focus is on the analysis and on numerical methods for problems with machine-learned components. For a rather general context, an error analysis … Read more

A Survey on Mixed-Integer Programming Techniques in Bilevel Optimization

Published: 2021/01/01, Updated: 2021/04/13

(Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming applications, bilevel optimization, Branch-and-Bound, branch-and-cut, mixed-integer programming, survey

Bilevel optimization is a field of mathematical programming in which some variables are constrained to be the solution of another optimization problem. As a consequence, bilevel optimization is able to model hierarchical decision processes. This is appealing for modeling real-world problems, but it also makes the resulting optimization models hard to solve in theory and … Read more

Constrained and Composite Optimization via Adaptive Sampling Methods

Published: 2020/12/30

Convex and Nonsmooth Optimization, Nonlinear Optimization, Stochastic Programming

The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method proposed in this paper is a proximal gradient method that can also be applied to the composite optimization problem min f(x) … Read more

Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications

Published: 2020/12/29

Fatma Kılınç-Karzan

Simge Küçükyavuz

Dabeen Lee

(Mixed) Integer Nonlinear Programming best subset selection, conic mixed-binary sets, conic quadratic optimization, convex hull, distributionally robust optimization, extended polymatroid inequalities, fractional binary optimization, submodularity

We consider a general conic mixed-binary set where each homogeneous conic constraint involves an affine function of independent continuous variables and an epigraph variable associated with a nonnegative function, $f_j$, of common binary variables. Sets of this form naturally arise as substructures in a number of applications including mean-risk optimization, chance-constrained problems, portfolio optimization, lot-sizing … Read more