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Bi-objective optimization problems on matroids are in general intractable and their corresponding decision problems are in general NP-hard. However, if one of the objective functions is restricted to binary cost coefficients the problem…
Finding a maximum cardinality common independent set in two matroids (also known as \textsc{Matroid Intersection}) is a classical combinatorial optimization problem, which generalizes several well-known problems, such as finding a maximum…
Multi-objective optimization models that encode ordered sequential constraints provide a solution to model various challenging problems including encoding preferences, modeling a curriculum, and enforcing measures of safety. A recently…
Deep learning models form one of the most powerful machine learning models for the extraction of important features. Most of the designs of deep neural models, i.e., the initialization of parameters, are still manually tuned. Hence,…
Set partitioning is a key component of many algorithms in machine learning, signal processing, and communications. In general, the problem of finding a partition that minimizes a given impurity (loss function) is NP-hard. As such, there…
We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the…
Classification, recommendation, and ranking problems often involve competing goals with additional constraints (e.g., to satisfy fairness or diversity criteria). Such optimization problems are quite challenging, often involving non-convex…
For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a…
Matroid intersection is a classical optimization problem where, given two matroids over the same ground set, the goal is to find the largest common independent set. In this paper, we show that there exists a certain "sparsifer": a subset of…
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and…
This paper studies a dynamic real-time optimization in the context of model-based time-optimal operation of batch processes under parametric model mismatch. In order to tackle the model-mismatch issue, a receding-horizon policy is usually…
This paper considers sparse polynomial optimization with unbounded sets. When the problem possesses correlative sparsity, we propose a sparse homogenized Moment-SOS hierarchy with perturbations to solve it. The new hierarchy introduces one…
This paper introduces algorithms for problems where a decision maker has to control a system composed of several components and has access to only partial information on the state of each component. Such problems are difficult because of…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
Which ads should we display in sponsored search in order to maximize our revenue? How should we dynamically rank information sources to maximize the value of the ranking? These applications exhibit strong diminishing returns: Redundancy…
A major difficulty of solving continuous POMDPs is to infer the multi-modal distribution of the unobserved true states and to make the planning algorithm dependent on the perceived uncertainty. We cast POMDP filtering and planning problems…
Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…
In this article, we use the monotonic optimization approach to propose an outcome-space outer approximation by copolyblocks for solving strictly quasiconvex multiobjective programming problems and especially in the case that the objective…
In many operations management problems, we need to make decisions sequentially to minimize the cost while satisfying certain constraints. One modeling approach to study such problems is constrained Markov decision process (CMDP). When…
Result diversification is an important aspect in web-based search, document summarization, facility location, portfolio management and other applications. Given a set of ranked results for a set of objects (e.g. web documents, facilities,…