Optimization with learning-informed differential equation constraints and its applications

Categories 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

Efficient presolving methods for the influence maximization problem in social networks

Categories (Mixed) Integer Linear Programming Tags , , , , ,

We consider the influence maximization problem (IMP) which asks for identifying a limited number of key individuals to spread influence in a social network such that the expected number of influenced individuals is maximized. The stochastic maximal covering location problem (SMCLP) formulation is a mixed integer programming formulation that effectively approximates the IMP by the … Read more

Constrained and Composite Optimization via Adaptive Sampling Methods

Categories 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

Supermodularity and valid inequalities for quadratic optimization with indicators

Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming Tags , , , , ,

We study the minimization of a rank-one quadratic with indicators and show that the underlying set function obtained by projecting out the continuous variables is supermodular. Although supermodular minimization is, in general, difficult, the specific set function for the rank-one quadratic can be minimized in linear time. We show that the convex hull of the … Read more

Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications

Categories (Mixed) Integer Nonlinear Programming Tags , , , , , , ,

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

Weak notions of nondegeneracy in nonlinear semidefinite programming

Categories Constrained Nonlinear Optimization, Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , ,

The constraint nondegeneracy condition is one of the most relevant and useful constraint qualifications in nonlinear semidefinite programming. It can be characterized in terms of any fixed orthonormal basis of the, let us say, $\ell$-dimensional kernel of the constraint matrix, by the linear independence of a set of $\ell(\ell+1)/2$ derivative vectors. We show that this … Read more

Fleet Sizing and Service Region Partitioning for Same-Day Delivery Systems

Categories Applications - OR and Management Sciences, Transportation Tags , , ,

We study the linked tactical design problems of fleet sizing and partitioning a service region into vehicle routing zones for same-day delivery (SDD) systems. Existing SDD studies focus primarily on operational dispatch problems and do not consider system design questions. Prior work on SDD system design has not considered the fleet sizing decision when a … Read more

A new branch-and-filter exact algorithm for binary constraint satisfaction problems

Categories Applications - OR and Management Sciences, Combinatorial Optimization Tags , , ,

A binary constraint satisfaction problem (BCSP) consist in determining an assignment of values to variables which is compatible with a set of constraints. The problem is called binary because the constraints involve only pairs of variables. The BCSP is a cornerstone problem in Constraint Programming (CP), appearing in a very wide range of real-world applications. … Read more

The Landscape of the Proximal Point Method for Nonconvex-Nonconcave Minimax Optimization

Categories Robust Optimization, Unconstrained Optimization Tags , , , , , ,

Minimax optimization has become a central tool for modern machine learning with applications in generative adversarial networks, robust optimization, reinforcement learning, etc. These applications are often nonconvex-nonconcave, but the existing theory is unable to identify and deal with the fundamental difficulties posed by nonconvex-nonconcave structures. In this paper, we study the classic proximal point method … Read more

Error bounds, facial residual functions and applications to the exponential cone

Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

We construct a general framework for deriving error bounds for conic feasibility problems. In particular, our approach allows one to work with cones that fail to be amenable or even to have computable projections, two previously challenging barriers. For the purpose, we first show how error bounds may be constructed using objects called one-step facial … Read more