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We focus on establishing the foundational paradigm of a novel optimization theory based on convolution with convex kernels. Our goal is to devise a morally deterministic model of locating the global optima of an arbitrary function, which is…
Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a…
We make progress towards understanding the structure of Littlewood-Richardson coefficients $g_{\lambda,\mu}^{\nu}$ for products of Jack symmetric functions. Building on recent results of the second author, we are able to prove new cases of…
In robust decision-making under non-Bayesian uncertainty, different robust optimization criteria, such as maximin performance, minimax regret, and maximin ratio, have been proposed. In many problems, all three criteria are well-motivated…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of…
Constrained decision-making is essential for designing safe policies in real-world control systems, yet simulated environments often fail to capture real-world adversities. We consider the problem of learning a policy that will maximize the…
A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…
The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the…
This paper considers the problem of maximizing multiple linear functions over the probability simplex. A classification of feasible points is indicated. A necessary and sufficient condition for a member of each class to be an efficient…
Mathematical optimization, although often leading to NP-hard models, is now capable of solving even large-scale instances within reasonable time. However, the primary focus is often placed solely on optimality. This implies that while…
An agent who lacks preferences and instead makes decisions using criteria that are costly to create should select efficient sets of criteria, where the cost of making a given number of choice distinctions is minimized. Under mild…
Hyperbolic spaces have been quite popular in the recent past for representing hierarchically organized data. Further, several classification algorithms for data in these spaces have been proposed in the literature. These algorithms mainly…
We effectively bound T-singularities on non-rational projective surfaces with an arbitrary amount of T-singularities and ample canonical class. This fully generalizes the previous work for the case of one singularity, and illustrates the…
Predicting the value of a function $f$ at a new point given its values at old points is an ubiquitous scientific endeavor, somewhat less developed when $f$ produces multiple values that depend on one another, e.g. when it outputs…
An elegant characterization of the complexity of constraint satisfaction problems has emerged in the form of the the algebraic dichotomy conjecture of [BKJ00]. Roughly speaking, the characterization asserts that a CSP {\Lambda} is tractable…
The purpose of this paper is to propose and analyze a multi-step iterative algorithm to solve a convex optimization problem and a fixed point problem posed on a Hadamard space. The convergence properties of the proposed algorithm are…
Value function factorization has achieved great success in multi-agent reinforcement learning by optimizing joint action-value functions through the maximization of factorized per-agent utilities. To ensure Individual-Global-Maximum…
The scenario approach provides a powerful data-driven framework for designing solutions under uncertainty with rigorous probabilistic robustness guarantees. Existing theory, however, primarily addresses assessing robustness with respect to…
Programs to solve so-called constraint problems are complex pieces of software which require many design decisions to be made more or less arbitrarily by the implementer. These decisions affect the performance of the finished solver…
In this paper we investigate the optimal partition approach for multiparametric conic linear optimization (mpCLO) problems in which the objective function depends linearly on vectors. We first establish more useful properties of the…